Abstract
We equip $\mathrm {BP} \langle n \rangle $ with an $\mathbb {E}_3$-$\mathrm{BP}$-algebra structure for each prime $p$ and height $n$. The algebraic $K$-theory of this ring is of chromatic height exactly $n+1$, and the map $\mathrm {K}(\mathrm{BP}\langle n \rangle )_{(p)} \to \mathrm {L}_{n+1}^{f} \mathrm {K}(\mathrm {BP}\langle n\rangle )_{(p)}$ has bounded above fiber.
-
[adams-periodicity]
J. F. Adams, "A periodicity theorem in homological algebra," Proc. Cambridge Philos. Soc., vol. 62, pp. 365-377, 1966.@ARTICLE{adams-periodicity,
author = {Adams, J. F.},
title = {A periodicity theorem in homological algebra},
journal = {Proc. Cambridge Philos. Soc.},
fjournal = {Proceedings of the Cambridge Philosophical Society},
volume = {62},
year = {1966},
pages = {365--377},
issn = {0008-1981},
mrclass = {18.20},
mrnumber = {0194486},
mrreviewer = {R. M. F. Moss},
doi = {10.1017/s0305004100039955},
url = {https://doi.org/10.1017/s0305004100039955},
zblnumber = {0163.01602},
} -
[gunawardena] J. F. Adams, J. H. Gunawardena, and H. Miller, "The Segal conjecture for elementary abelian $p$-groups," Topology, vol. 24, iss. 4, pp. 435-460, 1985.
@ARTICLE{gunawardena,
author = {Adams, J. F. and Gunawardena, J. H. and Miller, H.},
title = {The {S}egal conjecture for elementary abelian {$p$}-groups},
journal = {Topology},
fjournal = {Topology. An International Journal of Mathematics},
volume = {24},
year = {1985},
number = {4},
pages = {435--460},
issn = {0040-9383},
mrclass = {55T15 (55P42 55R35 57S17)},
mrnumber = {0816524},
mrreviewer = {J. P. May},
doi = {10.1016/0040-9383(85)90014-X},
url = {https://doi.org/10.1016/0040-9383(85)90014-X},
zblnumber = {0611.55010},
} -
[angeliniknollbeta] G. Angelini-Knoll, Detecting $\beta$ elements in iterated algebraic K-theory, 2021.
@MISC{angeliniknollbeta,
author = {Angelini-Knoll, Gabriel},
title = {Detecting {$\beta$} elements in iterated algebraic {K}-theory},
year = {2021},
arxiv = {1810.10088},
zblnumber = {},
} -
[angeliniknoll-quigley-segal] G. Angelini-Knoll and J. D. Quigley, "The Segal conjecture for topological Hochschild homology of Ravenel spectra," J. Homotopy Relat. Struct., vol. 16, iss. 1, pp. 41-60, 2021.
@ARTICLE{angeliniknoll-quigley-segal,
author = {Angelini-Knoll, Gabriel and Quigley, J. D.},
title = {The {S}egal conjecture for topological {H}ochschild homology of {R}avenel spectra},
journal = {J. Homotopy Relat. Struct.},
fjournal = {Journal of Homotopy and Related Structures},
volume = {16},
year = {2021},
number = {1},
pages = {41--60},
issn = {2193-8407},
mrclass = {55P42 (18F25)},
mrnumber = {4225506},
mrreviewer = {Juan Antonio Pérez},
doi = {10.1007/s40062-021-00275-7},
url = {https://doi.org/10.1007/s40062-021-00275-7},
zblnumber = {1467.55007},
} -
[angelini-knoll-salch-maysseq] G. Angelini-Knoll and A. Salch, "A May-type spectral sequence for higher topological Hochschild homology," Algebr. Geom. Topol., vol. 18, iss. 5, pp. 2593-2660, 2018.
@ARTICLE{angelini-knoll-salch-maysseq,
author = {Angelini-Knoll, Gabriel and Salch, Andrew},
title = {A {M}ay-type spectral sequence for higher topological {H}ochschild homology},
journal = {Algebr. Geom. Topol.},
fjournal = {Algebraic \& Geometric Topology},
volume = {18},
year = {2018},
number = {5},
pages = {2593--2660},
issn = {1472-2747},
mrclass = {18G30 (19D55 55P42 55T05)},
mrnumber = {3848395},
mrreviewer = {Tyler D. Lawson},
doi = {10.2140/agt.2018.18.2593},
url = {https://doi.org/10.2140/agt.2018.18.2593},
zblnumber = {1410.18016},
} -
[angeliniknoll-quigley] G. Angelini-Knoll and J. D. Quigley, Chromatic complexity of the algebraic K-theory of $y(n)$, 2021.
@MISC{angeliniknoll-quigley,
author = {Angelini-Knoll, Gabriel and Quigley,J. D.},
title = {Chromatic complexity of the algebraic {K}-theory of $y(n)$},
year = {2021},
arxiv = {1908.09164},
zblnumber = {},
} -
[angel] V. Angeltveit, "Topological Hochschild homology and cohomology of $A_\infty$ ring spectra," Geom. Topol., vol. 12, iss. 2, pp. 987-1032, 2008.
@ARTICLE{angel,
author = {Angeltveit, Vigleik},
title = {Topological {H}ochschild homology and cohomology of {$A_\infty$} ring spectra},
journal = {Geom. Topol.},
fjournal = {Geometry \& Topology},
volume = {12},
year = {2008},
number = {2},
pages = {987--1032},
issn = {1465-3060},
mrclass = {55P43 (18D50 19D55 55S35)},
mrnumber = {2403804},
mrreviewer = {Andrey Yu. Lazarev},
doi = {10.2140/gt.2008.12.987},
url = {https://doi.org/10.2140/gt.2008.12.987},
zblnumber = {1149.55006},
} -
[angeltveit-hill-lawson] V. Angeltveit, M. A. Hill, and T. Lawson, "Topological Hochschild homology of $\ell$ and $k_o$," Amer. J. Math., vol. 132, iss. 2, pp. 297-330, 2010.
@ARTICLE{angeltveit-hill-lawson,
author = {Angeltveit, Vigleik and Hill, Michael A. and Lawson, Tyler},
title = {Topological {H}ochschild homology of {$\ell$} and {$k_o$}},
journal = {Amer. J. Math.},
fjournal = {American Journal of Mathematics},
volume = {132},
year = {2010},
number = {2},
pages = {297--330},
issn = {0002-9327},
mrclass = {19L41 (19D55 55N35 55P43)},
mrnumber = {2654776},
mrreviewer = {Jerry Lodder},
doi = {10.1353/ajm.0.0105},
url = {https://doi.org/10.1353/ajm.0.0105},
zblnumber = {1271.55009},
} -
[angeltveit-lind] V. Angeltveit and J. A. Lind, "Uniqueness of $BP \langle n\rangle$," J. Homotopy Relat. Struct., vol. 12, iss. 1, pp. 17-30, 2017.
@ARTICLE{angeltveit-lind,
author = {Angeltveit, Vigleik and Lind, John A.},
title = {Uniqueness of {$BP \langle n\rangle$}},
journal = {J. Homotopy Relat. Struct.},
fjournal = {Journal of Homotopy and Related Structures},
volume = {12},
year = {2017},
number = {1},
pages = {17--30},
issn = {2193-8407},
mrclass = {55P42 (55S10)},
mrnumber = {3613020},
mrreviewer = {Agnès Beaudry},
doi = {10.1007/s40062-015-0120-0},
url = {https://doi.org/10.1007/s40062-015-0120-0},
zblnumber = {1379.55007},
} -
[angeltveit-rognes] V. Angeltveit and J. Rognes, "Hopf algebra structure on topological Hochschild homology," Algebr. Geom. Topol., vol. 5, pp. 1223-1290, 2005.
@ARTICLE{angeltveit-rognes,
author = {Angeltveit, Vigleik and Rognes, John},
title = {Hopf algebra structure on topological {H}ochschild homology},
journal = {Algebr. Geom. Topol.},
fjournal = {Algebraic \& Geometric Topology},
volume = {5},
year = {2005},
pages = {1223--1290},
issn = {1472-2747},
mrclass = {55P43 (16W30 55S10 55S12 55T15 57T05)},
mrnumber = {2171809},
doi = {10.2140/agt.2005.5.1223},
url = {https://doi.org/10.2140/agt.2005.5.1223},
zblnumber = {1087.55009},
} -
[ammn-fiber] B. Antieau, A. Mathew, M. Morrow, and T. Nikolaus, On the Beilinson fiber square, 2021.
@MISC{ammn-fiber,
author = {Antieau, Benjamin and Mathew, A. and Morrow, M. and Nikolaus, T.},
title = {On the {B}eilinson fiber square},
year = {2021},
arxiv = {2003.12541},
} -
[antieau-nikolaus] B. Antieau and T. Nikolaus, "Cartier modules and cyclotomic spectra," J. Amer. Math. Soc., vol. 34, iss. 1, pp. 1-78, 2021.
@ARTICLE{antieau-nikolaus,
author = {Antieau, Benjamin and Nikolaus, Thomas},
title = {Cartier modules and cyclotomic spectra},
journal = {J. Amer. Math. Soc.},
fjournal = {Journal of the American Mathematical Society},
volume = {34},
year = {2021},
number = {1},
pages = {1--78},
issn = {0894-0347},
mrclass = {14F30 (13D03 14L05)},
mrnumber = {4188814},
mrreviewer = {Bhargav Bhatt},
doi = {10.1090/jams/951},
url = {https://doi.org/10.1090/jams/951},
zblnumber = {1467.14058},
} -
[ausonidescent] C. Ausoni, "Topological Hochschild homology of connective complex $K$-theory," Amer. J. Math., vol. 127, iss. 6, pp. 1261-1313, 2005.
@ARTICLE{ausonidescent,
author = {Ausoni, Christian},
title = {Topological {H}ochschild homology of connective complex {$K$}-theory},
journal = {Amer. J. Math.},
fjournal = {American Journal of Mathematics},
volume = {127},
year = {2005},
number = {6},
pages = {1261--1313},
issn = {0002-9327},
mrclass = {55P43 (19D55 19L41)},
mrnumber = {2183525},
mrreviewer = {Guillermo Corti\~{n}as},
doi = {10.1353/ajm.2005.0036},
url = {https://doi.org/10.1353/ajm.2005.0036},
zblnumber = {1107.55006},
} -
[ausoni-topk] C. Ausoni, "On the algebraic ${K}$-theory of the complex ${K}$-theory spectrum," Invent. Math., vol. 180, iss. 3, pp. 611-668, 2010.
@ARTICLE{ausoni-topk,
author = {Ausoni, Christian},
title = {On the algebraic {${K}$}-theory of the complex {${K}$}-theory spectrum},
journal = {Invent. Math.},
fjournal = {Inventiones Mathematicae},
volume = {180},
year = {2010},
number = {3},
pages = {611--668},
issn = {0020-9910},
mrclass = {19L41 (55N15 55P43)},
mrnumber = {2609252},
doi = {10.1007/s00222-010-0239-x},
url = {https://doi.org/10.1007/s00222-010-0239-x},
zblnumber = {1204.19002},
} -
[ausoni-richter] C. Ausoni and B. Richter, "Towards topological Hochschild homology of Johnson-Wilson spectra," Algebr. Geom. Topol., vol. 20, iss. 1, pp. 375-393, 2020.
@ARTICLE{ausoni-richter,
author = {Ausoni, Christian and Richter, Birgit},
title = {Towards topological {H}ochschild homology of {J}ohnson-{W}ilson spectra},
journal = {Algebr. Geom. Topol.},
fjournal = {Algebraic \& Geometric Topology},
volume = {20},
year = {2020},
number = {1},
pages = {375--393},
issn = {1472-2747},
mrclass = {55N35 (55P43)},
mrnumber = {4071375},
mrreviewer = {Inbar Klang},
doi = {10.2140/agt.2020.20.375},
url = {https://doi.org/10.2140/agt.2020.20.375},
zblnumber = {1437.55009},
} -
[ausoni-rognes-redshift] C. Ausoni and J. Rognes, "Algebraic $\mathrm{K}$-theory of topological $\mathrm{K}$-theory," Acta Math., vol. 188, iss. 1, pp. 1-39, 2002.
@ARTICLE{ausoni-rognes-redshift,
author = {Ausoni, Christian and Rognes, John},
title = {Algebraic {$\mathrm{K}$}-theory of topological {$\mathrm{K}$}-theory},
journal = {Acta Math.},
fjournal = {Acta Mathematica},
volume = {188},
year = {2002},
number = {1},
pages = {1--39},
issn = {0001-5962},
mrclass = {19D55 (19L20)},
mrnumber = {1947457},
mrreviewer = {Charles Weibel},
doi = {10.1007/BF02392794},
url = {https://doi.org/10.1007/BF02392794},
zblnumber = {1019.18008},
} -
[ausoni-rognes-height1] C. Ausoni and J. Rognes, "Algebraic $K$-theory of the first Morava $K$-theory," J. Eur. Math. Soc. (JEMS), vol. 14, iss. 4, pp. 1041-1079, 2012.
@ARTICLE{ausoni-rognes-height1,
author = {Ausoni, Christian and Rognes, John},
title = {Algebraic {$K$}-theory of the first {M}orava {$K$}-theory},
journal = {J. Eur. Math. Soc. (JEMS)},
fjournal = {Journal of the European Mathematical Society (JEMS)},
volume = {14},
year = {2012},
number = {4},
pages = {1041--1079},
issn = {1435-9855},
mrclass = {19L20 (19D55 19L41)},
mrnumber = {2928844},
mrreviewer = {Kyle M. Ormsby},
doi = {10.4171/JEMS/326},
url = {https://doi.org/10.4171/JEMS/326},
zblnumber = {1253.19001},
} -
[ausoni-rognes-rational] C. Ausoni and J. Rognes, "Rational algebraic $K$-theory of topological $K$-theory," Geom. Topol., vol. 16, iss. 4, pp. 2037-2065, 2012.
@ARTICLE{ausoni-rognes-rational,
author = {Ausoni, Christian and Rognes, John},
title = {Rational algebraic {$K$}-theory of topological {$K$}-theory},
journal = {Geom. Topol.},
fjournal = {Geometry \& Topology},
volume = {16},
year = {2012},
number = {4},
pages = {2037--2065},
issn = {1465-3060},
mrclass = {19Lxx},
mrnumber = {2975299},
mrreviewer = {Carla Farsi},
doi = {10.2140/gt.2012.16.2037},
url = {https://doi.org/10.2140/gt.2012.16.2037},
zblnumber = {1260.19004},
} -
[ayala-francis] D. Ayala and J. Francis, "Factorization homology of topological manifolds," J. Topol., vol. 8, iss. 4, pp. 1045-1084, 2015.
@ARTICLE{ayala-francis,
author = {Ayala, David and Francis, John},
title = {Factorization homology of topological manifolds},
journal = {J. Topol.},
fjournal = {Journal of Topology},
volume = {8},
year = {2015},
number = {4},
pages = {1045--1084},
issn = {1753-8416},
mrclass = {55U40 (57N35 57R19 57R56)},
mrnumber = {3431668},
mrreviewer = {Jason Stuart Hanson},
doi = {10.1112/jtopol/jtv028},
url = {https://doi.org/10.1112/jtopol/jtv028},
zblnumber = {1350.55009},
} -
[2-vect] N. A. Baas, B. I. Dundas, and J. Rognes, "Two-vector bundles and forms of elliptic cohomology," in Topology, Geometry and Quantum Field Theory, Cambridge Univ. Press, Cambridge, 2004, vol. 308, pp. 18-45.
@INCOLLECTION{2-vect,
author = {Baas, Nils A. and Dundas, Bjørn Ian and Rognes, John},
title = {Two-vector bundles and forms of elliptic cohomology},
booktitle = {Topology, Geometry and Quantum Field Theory},
series = {London Math. Soc. Lecture Note Ser.},
volume = {308},
pages = {18--45},
publisher = {Cambridge Univ. Press, Cambridge},
year = {2004},
mrclass = {55N34 (18D05 57T30)},
mrnumber = {2079370},
mrreviewer = {Mark Hovey},
doi = {10.1017/CBO9780511526398.005},
url = {https://doi.org/10.1017/CBO9780511526398.005},
zblnumber = {1106.55004},
} -
[baker-jeanneret] A. Baker and A. Jeanneret, "Brave new Hopf algebroids and extensions of $M$$U$-algebras," Homology Homotopy Appl., vol. 4, iss. 1, pp. 163-173, 2002.
@ARTICLE{baker-jeanneret,
author = {Baker, Andrew and Jeanneret, Alain},
title = {Brave new {H}opf algebroids and extensions of {$M$}{$U$}-algebras},
journal = {Homology Homotopy Appl.},
fjournal = {Homology, Homotopy and Applications},
volume = {4},
year = {2002},
number = {1},
pages = {163--173},
issn = {1532-0081},
mrclass = {55P43 (55N20)},
mrnumber = {1937961},
mrreviewer = {Richard John Steiner},
doi = {10.4310/hha.2002.v4.n1.a9},
url = {https://doi.org/10.4310/hha.2002.v4.n1.a9},
zblnumber = {1380.55009},
} -
[bm] M. Basterra and M. A. Mandell, "The multiplication on BP," J. Topol., vol. 6, iss. 2, pp. 285-310, 2013.
@ARTICLE{bm,
author = {Basterra, Maria and Mandell, Michael A.},
title = {The multiplication on {BP}},
journal = {J. Topol.},
fjournal = {Journal of Topology},
volume = {6},
year = {2013},
number = {2},
pages = {285--310},
issn = {1753-8416},
mrclass = {55P43 (55N22 55S35)},
mrnumber = {3065177},
mrreviewer = {Jes\'{u}s Gonz\'{a}lez},
doi = {10.1112/jtopol/jts032},
url = {https://doi.org/10.1112/jtopol/jts032},
zblnumber = {1317.55005},
} -
[blumberg-cohen-schlichtkrull] A. J. Blumberg, R. L. Cohen, and C. Schlichtkrull, "Topological Hochschild homology of Thom spectra and the free loop space," Geom. Topol., vol. 14, iss. 2, pp. 1165-1242, 2010.
@ARTICLE{blumberg-cohen-schlichtkrull,
author = {Blumberg, Andrew J. and Cohen, Ralph L. and Schlichtkrull, Christian},
title = {Topological {H}ochschild homology of {T}hom spectra and the free loop space},
journal = {Geom. Topol.},
fjournal = {Geometry \& Topology},
volume = {14},
year = {2010},
number = {2},
pages = {1165--1242},
issn = {1465-3060},
mrclass = {55P43 (18G55 19D55 55N20 55P47 55R25)},
mrnumber = {2651551},
mrreviewer = {Rui Miguel Saramago},
doi = {10.2140/gt.2010.14.1165},
url = {https://doi.org/10.2140/gt.2010.14.1165},
zblnumber = {1219.19006},
} -
[bgt] A. J. Blumberg, D. Gepner, and G. Tabuada, "Uniqueness of the multiplicative cyclotomic trace," Adv. Math., vol. 260, pp. 191-232, 2014.
@ARTICLE{bgt,
author = {Blumberg, Andrew J. and Gepner, David and Tabuada, Gonçalo},
title = {Uniqueness of the multiplicative cyclotomic trace},
journal = {Adv. Math.},
fjournal = {Advances in Mathematics},
volume = {260},
year = {2014},
pages = {191--232},
issn = {0001-8708},
mrclass = {19D55 (19D23 55N15)},
mrnumber = {3209352},
mrreviewer = {Jeffrey Giansiracusa},
doi = {10.1016/j.aim.2014.02.004},
url = {https://doi.org/10.1016/j.aim.2014.02.004},
zblnumber = {1297.19002},
} -
[blumberg-mandell] A. J. Blumberg and M. A. Mandell, "The localization sequence for the algebraic $K$-theory of topological $K$-theory," Acta Math., vol. 200, iss. 2, pp. 155-179, 2008.
@ARTICLE{blumberg-mandell,
author = {Blumberg, Andrew J. and Mandell, Michael A.},
title = {The localization sequence for the algebraic {$K$}-theory of topological {$K$}-theory},
journal = {Acta Math.},
fjournal = {Acta Mathematica},
volume = {200},
year = {2008},
number = {2},
pages = {155--179},
issn = {0001-5962},
mrclass = {19D10 (55P43)},
mrnumber = {2413133},
mrreviewer = {Ian Hambleton},
doi = {10.1007/s11511-008-0025-4},
url = {https://doi.org/10.1007/s11511-008-0025-4},
zblnumber = {1149.18008},
} -
[boardman] M. J. Boardman, "Conditionally convergent spectral sequences," in Homotopy Invariant Algebraic Structures, Amer. Math. Soc., Providence, RI, 1999, vol. 239, pp. 49-84.
@INCOLLECTION{boardman,
author = {Boardman, J. Michael},
title = {Conditionally convergent spectral sequences},
booktitle = {Homotopy Invariant Algebraic Structures},
venue = {{B}altimore, {MD},
1998},
series = {Contemp. Math.},
volume = {239},
pages = {49--84},
publisher = {Amer. Math. Soc., Providence, RI},
year = {1999},
mrclass = {55T05 (18A30 18G40)},
mrnumber = {1718076},
mrreviewer = {John McCleary},
doi = {10.1090/conm/239/03597},
url = {https://doi.org/10.1090/conm/239/03597},
zblnumber = {0947.55020},
} -
[BokstedtMadsen] M. Bökstedt and I. Madsen, "Topological cyclic homology of the integers," in $\mathrm{K}$-Theory, , 1994, vol. 226, pp. 57-143.
@INCOLLECTION{BokstedtMadsen,
author = {Bökstedt, M. and Madsen, I.},
title = {Topological cyclic homology of the integers},
booktitle = {$\mathrm{K}$-Theory},
venue = {Strasbourg, 1992},
series = {Astérisque},
volume = {226},
year = {1994},
pages = {57--143},
issn = {0303-1179},
mrclass = {19D50 (19D55 55P91)},
mrnumber = {1317117},
mrreviewer = {J. P. May},
zblnumber = {0816.19001},
url = {http://www.numdam.org/item/AST_1994__226__57_0/},
} -
[bousfield] A. K. Bousfield, "The localization of spectra with respect to homology," Topology, vol. 18, iss. 4, pp. 257-281, 1979.
@ARTICLE{bousfield,
author = {Bousfield, A. K.},
title = {The localization of spectra with respect to homology},
journal = {Topology},
fjournal = {Topology. An International Journal of Mathematics},
volume = {18},
year = {1979},
number = {4},
pages = {257--281},
issn = {0040-9383},
mrclass = {55N20 (55N15 55P60)},
mrnumber = {0551009},
mrreviewer = {Willi Meier},
doi = {10.1016/0040-9383(79)90018-1},
url = {https://doi.org/10.1016/0040-9383(79)90018-1},
zblnumber = {0417.55007},
} -
[hinfty] R. R. Bruner, J. P. May, J. E. McClure, and M. Steinberger, $H_\infty $ Ring Spectra and their Applications, Springer-Verlag, Berlin, 1986, vol. 1176.
@BOOK{hinfty,
author = {Bruner, R. R. and May, J. P. and McClure, J. E. and Steinberger, M.},
title = {{$H_\infty $} Ring Spectra and their Applications},
series = {Lecture Notes in Math.},
volume = {1176},
publisher = {Springer-Verlag, Berlin},
year = {1986},
pages = {viii+388},
isbn = {3-540-16434-0},
mrclass = {55-02 (55P42 55Sxx)},
mrnumber = {0836132},
mrreviewer = {Haynes R. Miller},
doi = {10.1007/BFb0075405},
url = {https://doi.org/10.1007/BFb0075405},
zblnumber = {0585.55016},
} -
[burklund-hahn-senger] R. Burklund, J. Hahn, and A. Senger, Galois reconstruction of Artin-Tate $\mathbb{R}$-motivic spectra, 2020.
@MISC{burklund-hahn-senger,
author = {Burklund, R. and Hahn, J. and Senger, A.},
title = {Galois reconstruction of {A}rtin-{T}ate $\mathbb{R}$-motivic spectra},
year = {2020},
arxiv = {2010.10325},
zblnumber = {},
} -
[carmelischlankyanovski] S. Carmeli, T. M. Schlank, and L. Yanovski, "Ambidexterity and height," Adv. Math., vol. 385, p. 107763, 2021.
@ARTICLE{carmelischlankyanovski,
author = {Carmeli, Shachar and Schlank, Tomer M. and Yanovski, Lior},
title = {Ambidexterity and height},
journal = {Adv. Math.},
fjournal = {Advances in Mathematics},
volume = {385},
year = {2021},
pages = {Paper No. 107763, 90},
issn = {0001-8708},
mrclass = {18N60 (55U35)},
mrnumber = {4246977},
url = {https://doi.org/10.1016/j.aim.2021.107763},
zblnumber = {1466.18014},
} -
[cmnn] D. Clausen, A. Mathew, N. Naumann, and J. Noel, Descent and vanishing in chromatic algebraic $K$-theory via group actions, 2020.
@MISC{cmnn,
author = {Clausen, D. and Mathew, A. and Naumann, N. and Noel, J.},
title = {Descent and vanishing in chromatic algebraic {$K$}-theory via group actions},
year = {2020},
arxiv = {2011.08233},
zblnumber = {},
} -
[deligne] P. Deligne, "Théorie de Hodge. II," Inst. Hautes Études Sci. Publ. Math., iss. 40, pp. 5-57, 1971.
@ARTICLE{deligne,
author = {Deligne, Pierre},
title = {Théorie de {H}odge. {II}},
journal = {Inst. Hautes \'{E}tudes Sci. Publ. Math.},
fjournal = {Institut des Hautes \'{E}tudes Scientifiques. Publications Mathématiques},
number = {40},
year = {1971},
pages = {5--57},
issn = {0073-8301},
mrclass = {14C30 (14F15)},
mrnumber = {0498551},
mrreviewer = {J. H. M. Steenbrink},
url = {http://www.numdam.org/item?id=PMIHES_1971__40__5_0},
zblnumber = {0219.14007},
} -
[DGM-book] B. I. Dundas, T. G. Goodwillie, and R. McCarthy, The Local Structure of Algebraic $\mathrm{K}$-Theory, Springer-Verlag London, Ltd., London, 2013, vol. 18.
@BOOK{DGM-book,
author = {Dundas, Bjørn Ian and Goodwillie, Thomas G. and McCarthy, Randy},
title = {The Local Structure of Algebraic {$\mathrm{K}$}-Theory},
series = {Algebra Appl.},
volume = {18},
publisher = {Springer-Verlag London, Ltd., London},
year = {2013},
pages = {xvi+435},
isbn = {978-1-4471-4392-5; 978-1-4471-4393-2},
mrclass = {19-02 (16E40 19D55 55-02 55N99)},
mrnumber = {3013261},
mrreviewer = {Charles Weibel},
zblnumber = {1272.55002},
doi = {10.1007/978-1-4471/4393-2},
url = {https://doi.org/10.1007/978-1-4471-4393-2},
} -
[kupers-galatius-randall-williams] S. Galatius, A. Kupers, and O. Randal-Williams, Cellular $E_k$-algebras, 2021.
@MISC{kupers-galatius-randall-williams,
author = {Galatius, S. and Kupers, A. and Randal-Williams, O.},
title = {Cellular {$E_k$}-algebras},
year = {2021},
arxiv = {1805.07184},
zblnumber = {},
} -
[glasman-lawson] S. Glasman and T. Lawson, Stable power operations, 2020.
@MISC{glasman-lawson,
author = {Glasman, S. and Lawson, T.},
title = {{S}table power operations},
year = {2020},
arxiv = {2002.02035},
zblnumber = {},
} -
[greenlees-may] J. P. C. Greenlees and J. P. May, "Generalized Tate cohomology," Mem. Amer. Math. Soc., vol. 113, iss. 543, p. viii, 1995.
@ARTICLE{greenlees-may,
author = {Greenlees, J. P. C. and May, J. P.},
title = {Generalized {T}ate cohomology},
journal = {Mem. Amer. Math. Soc.},
fjournal = {Memoirs of the American Mathematical Society},
volume = {113},
year = {1995},
number = {543},
pages = {viii+178},
issn = {0065-9266},
mrclass = {55N15 (19L47 55P42 55Q91 55T25)},
mrnumber = {1230773},
mrreviewer = {V. P. Snaith},
doi = {10.1090/memo/0543},
url = {https://doi.org/10.1090/memo/0543},
zblnumber = {0876.55003},
} -
[harpaz-nuiten-prasma] Y. Harpaz, J. Nuiten, and M. Prasma, "Tangent categories of algebras over operads," Israel J. Math., vol. 234, iss. 2, pp. 691-742, 2019.
@ARTICLE{harpaz-nuiten-prasma,
author = {Harpaz, Yonatan and Nuiten, Joost and Prasma, Matan},
title = {Tangent categories of algebras over operads},
journal = {Israel J. Math.},
fjournal = {Israel Journal of Mathematics},
volume = {234},
year = {2019},
number = {2},
pages = {691--742},
issn = {0021-2172},
mrclass = {55P48 (18M60)},
mrnumber = {4040842},
mrreviewer = {N. C. Combe},
doi = {10.1007/s11856-019-1933-z},
url = {https://doi.org/10.1007/s11856-019-1933-z},
zblnumber = {1435.55010},
} -
[hedenlund] A. P. Hedenlund, Multiplicative Tate spectral sequences, 2020.
@MISC{hedenlund,
author = {Hedenlund, A. P.},
title = {Multiplicative {T}ate spectral sequences},
year = {2020},
note = {{T}hesis (Ph.D.)--Univ. of Oslo; available on John Rognes' website},
zblnumber = {},
} -
[hesselholt] L. Hesselholt, "Topological Hochschild homology and the Hasse-Weil zeta function," in An Alpine Bouquet of Algebraic Topology, Amer. Math. Soc., Providence, RI, 2018, vol. 708, pp. 157-180.
@INCOLLECTION{hesselholt,
author = {Hesselholt, Lars},
title = {Topological {H}ochschild homology and the {H}asse-{W}eil zeta function},
booktitle = {An Alpine Bouquet of Algebraic Topology},
series = {Contemp. Math.},
volume = {708},
pages = {157--180},
publisher = {Amer. Math. Soc., Providence, RI},
year = {2018},
mrclass = {11S40 (14F30 19D55)},
mrnumber = {3807755},
mrreviewer = {Cid Reyes-Bustos},
doi = {10.1090/conm/708/14264},
url = {https://doi.org/10.1090/conm/708/14264},
zblnumber = {1402.19002},
} -
[hesselholt-madsen] L. Hesselholt and I. Madsen, "On the $K$-theory of local fields," Ann. of Math. (2), vol. 158, iss. 1, pp. 1-113, 2003.
@ARTICLE{hesselholt-madsen,
author = {Hesselholt, Lars and Madsen, Ib},
title = {On the {$K$}-theory of local fields},
journal = {Ann. of Math. (2)},
fjournal = {Annals of Mathematics. Second Series},
volume = {158},
year = {2003},
number = {1},
pages = {1--113},
issn = {0003-486X},
mrclass = {19D50 (11S70 13K05 19D55 19F05 55P91)},
mrnumber = {1998478},
mrreviewer = {J. P. C. Greenlees},
doi = {10.4007/annals.2003.158.1},
url = {https://doi.org/10.4007/annals.2003.158.1},
zblnumber = {1033.19002},
} -
[hesselholt-madsen-derham] L. Hesselholt and I. Madsen, "On the de Rham-Witt complex in mixed characteristic," Ann. Sci. École Norm. Sup. (4), vol. 37, iss. 1, pp. 1-43, 2004.
@ARTICLE{hesselholt-madsen-derham,
author = {Hesselholt, Lars and Madsen, Ib},
title = {On the de {R}ham-{W}itt complex in mixed characteristic},
journal = {Ann. Sci. \'{E}cole Norm. Sup. (4)},
fjournal = {Annales Scientifiques de l'\'{E}cole Normale Supérieure. Quatrième Série},
volume = {37},
year = {2004},
number = {1},
pages = {1--43},
issn = {0012-9593},
mrclass = {19D50 (16E45)},
mrnumber = {2050204},
mrreviewer = {Kevin P. Knudson},
doi = {10.1016/j.ansens.2003.06.001},
url = {https://doi.org/10.1016/j.ansens.2003.06.001},
zblnumber = {1062.19003},
} -
[hill-lawson] M. Hill and T. Lawson, "Automorphic forms and cohomology theories on Shimura curves of small discriminant," Adv. Math., vol. 225, iss. 2, pp. 1013-1045, 2010.
@ARTICLE{hill-lawson,
author = {Hill, Michael and Lawson, Tyler},
title = {Automorphic forms and cohomology theories on {S}himura curves of small discriminant},
journal = {Adv. Math.},
fjournal = {Advances in Mathematics},
volume = {225},
year = {2010},
number = {2},
pages = {1013--1045},
issn = {0001-8708},
mrclass = {55P43 (11F23 11G18 14G35 55P42)},
mrnumber = {2671186},
mrreviewer = {Paul G. Goerss},
doi = {10.1016/j.aim.2010.03.009},
url = {https://doi.org/10.1016/j.aim.2010.03.009},
zblnumber = {1220.55006},
} -
[hopkins-palmieri-smith] M. J. Hopkins, J. H. Palmieri, and J. H. Smith, "Vanishing lines in generalized Adams spectral sequences are generic," Geom. Topol., vol. 3, pp. 155-165, 1999.
@ARTICLE{hopkins-palmieri-smith,
author = {Hopkins, M. J. and Palmieri, J. H. and Smith, J. H.},
title = {Vanishing lines in generalized {A}dams spectral sequences are generic},
journal = {Geom. Topol.},
fjournal = {Geometry and Topology},
volume = {3},
year = {1999},
pages = {155--165},
issn = {1465-3060},
mrclass = {55T15 (55P42)},
mrnumber = {1697180},
mrreviewer = {Neil P. Strickland},
doi = {10.2140/gt.1999.3.155},
url = {https://doi.org/10.2140/gt.1999.3.155},
zblnumber = {0920.55020},
} -
[hopkins-smith] M. J. Hopkins and J. H. Smith, "Nilpotence and stable homotopy theory. II," Ann. of Math. (2), vol. 148, iss. 1, pp. 1-49, 1998.
@ARTICLE{hopkins-smith,
author = {Hopkins, Michael J. and Smith, Jeffrey H.},
title = {Nilpotence and stable homotopy theory. {II}},
journal = {Ann. of Math. (2)},
fjournal = {Annals of Mathematics. Second Series},
volume = {148},
year = {1998},
number = {1},
pages = {1--49},
issn = {0003-486X},
mrclass = {55P42 (55N20 55Q10)},
mrnumber = {1652975},
mrreviewer = {David A. Blanc},
doi = {10.2307/120991},
url = {https://doi.org/10.2307/120991},
zblnumber = {0924.55010},
} -
[hovey-splitting] M. Hovey, "Bousfield localization functors and Hopkins’ chromatic splitting conjecture," in The \vCech Centennial, Amer. Math. Soc., Providence, RI, 1995, vol. 181, pp. 225-250.
@INCOLLECTION{hovey-splitting,
author = {Hovey, Mark},
title = {Bousfield localization functors and {H}opkins' chromatic splitting conjecture},
booktitle = {The {\v{C}}ech Centennial},
venue = {{B}oston, {MA},
1993},
series = {Contemp. Math.},
volume = {181},
pages = {225--250},
publisher = {Amer. Math. Soc., Providence, RI},
year = {1995},
mrclass = {55P42 (55N20 55N22 55P60)},
mrnumber = {1320994},
doi = {10.1090/conm/181/02036},
url = {https://doi.org/10.1090/conm/181/02036},
zblnumber = {0830.55004},
} -
[hovey-vn] M. A. Hovey, "$v_n$-elements in ring spectra and applications to bordism theory," Duke Math. J., vol. 88, iss. 2, pp. 327-356, 1997.
@ARTICLE{hovey-vn,
author = {Hovey, Mark A.},
title = {{$v_n$}-elements in ring spectra and applications to bordism theory},
journal = {Duke Math. J.},
fjournal = {Duke Mathematical Journal},
volume = {88},
year = {1997},
number = {2},
pages = {327--356},
issn = {0012-7094},
mrclass = {55P60 (55N22)},
mrnumber = {1455523},
mrreviewer = {R. E. Stong},
doi = {10.1215/S0012-7094-97-08813-X},
url = {https://doi.org/10.1215/S0012-7094-97-08813-X},
zblnumber = {0880.55006},
} -
[kitchloo-lorman-wilson] N. Kitchloo, V. Lorman, and S. W. Wilson, "Multiplicative structure on real Johnson-Wilson theory," in New Directions in Homotopy Theory, Amer. Math. Soc., Providence, RI, 2018, vol. 707, pp. 31-44.
@INCOLLECTION{kitchloo-lorman-wilson,
author = {Kitchloo, Nitu and Lorman, Vitaly and Wilson, W. Stephen},
title = {Multiplicative structure on real {J}ohnson-{W}ilson theory},
booktitle = {New {D}irections in {H}omotopy {T}heory},
series = {Contemp. Math.},
volume = {707},
pages = {31--44},
publisher = {Amer. Math. Soc., Providence, RI},
year = {2018},
mrclass = {55P91 (55N22 55N91)},
mrnumber = {3807740},
mrreviewer = {Samik Basu},
doi = {10.1090/conm/707/14252},
url = {https://doi.org/10.1090/conm/707/14252},
zblnumber = {1404.55015},
} -
[kochman] S. O. Kochman, "Homology of the classical groups over the Dyer-Lashof algebra," Trans. Amer. Math. Soc., vol. 185, pp. 83-136, 1973.
@ARTICLE{kochman,
author = {Kochman, Stanley O.},
title = {Homology of the classical groups over the {D}yer-{L}ashof algebra},
journal = {Trans. Amer. Math. Soc.},
fjournal = {Transactions of the American Mathematical Society},
volume = {185},
year = {1973},
pages = {83--136},
issn = {0002-9947},
mrclass = {55F45 (55G99)},
mrnumber = {0331386},
mrreviewer = {R. K. Lashof},
doi = {10.2307/1996429},
url = {https://doi.org/10.2307/1996429},
zblnumber = {0271.57013},
} -
[lmmt] M. Land, A. Mathew, L. Meier, and G. Tamme, Purity in chromatically localized algebraic $K$-theory, 2022.
@MISC{lmmt,
author = {Land, M. and Mathew, A. and Meier, L. and Tamme, G.},
title = {Purity in chromatically localized algebraic {$K$}-theory},
year = {2022},
arxiv = {2001.10425},
} -
[LawsonBP] T. Lawson, "Secondary power operations and the Brown-Peterson spectrum at the prime 2," Ann. of Math. (2), vol. 188, iss. 2, pp. 513-576, 2018.
@ARTICLE{LawsonBP,
author = {Lawson, Tyler},
title = {Secondary power operations and the {B}rown-{P}eterson spectrum at the prime 2},
journal = {Ann. of Math. (2)},
fjournal = {Annals of Mathematics. Second Series},
volume = {188},
year = {2018},
number = {2},
pages = {513--576},
issn = {0003-486X},
mrclass = {55P43 (55N22 55S12 55S20)},
mrnumber = {3862946},
mrreviewer = {Lennart Meier},
doi = {10.4007/annals.2018.188.2.3},
url = {https://doi.org/10.4007/annals.2018.188.2.3},
zblnumber = {1431.55011},
} -
[lawson-naumann] T. Lawson and N. Naumann, "Commutativity conditions for truncated Brown-Peterson spectra of height 2," J. Topol., vol. 5, iss. 1, pp. 137-168, 2012.
@ARTICLE{lawson-naumann,
author = {Lawson, Tyler and Naumann, Niko},
title = {Commutativity conditions for truncated {B}rown-{P}eterson spectra of height 2},
journal = {J. Topol.},
fjournal = {Journal of Topology},
volume = {5},
year = {2012},
number = {1},
pages = {137--168},
issn = {1753-8416},
mrclass = {55P42 (55N22 55N34 55P43)},
mrnumber = {2897051},
mrreviewer = {Rui Miguel Saramago},
doi = {10.1112/jtopol/jtr030},
url = {https://doi.org/10.1112/jtopol/jtr030},
zblnumber = {1280.55007},
} -
[lazarev] A. Lazarev, "Homotopy theory of $A_\infty$ ring spectra and applications to $MU$-modules," $K$-Theory, vol. 24, iss. 3, pp. 243-281, 2001.
@ARTICLE{lazarev,
author = {Lazarev, A.},
title = {Homotopy theory of {$A_\infty$} ring spectra and applications to {$MU$}-modules},
journal = {$K$-Theory},
fjournal = {$K$-Theory. An Interdisciplinary Journal for the Development, Application, and Influence of $K$-Theory in the Mathematical Sciences},
volume = {24},
year = {2001},
number = {3},
pages = {243--281},
issn = {0920-3036},
mrclass = {55P43 (55N20 55P42 55S35 55T25)},
mrnumber = {1876800},
mrreviewer = {Andrew J. Baker},
doi = {10.1023/A:1013394125552},
url = {https://doi.org/10.1023/A:1013394125552},
zblnumber = {1008.55007},
} -
[lin] W. H. Lin, "On conjectures of Mahowald, Segal and Sullivan," Math. Proc. Cambridge Philos. Soc., vol. 87, iss. 3, pp. 449-458, 1980.
@ARTICLE{lin,
author = {Lin, Wen Hsiung},
title = {On conjectures of {M}ahowald, {S}egal and {S}ullivan},
journal = {Math. Proc. Cambridge Philos. Soc.},
fjournal = {Mathematical Proceedings of the Cambridge Philosophical Society},
volume = {87},
year = {1980},
number = {3},
pages = {449--458},
issn = {0305-0041},
mrclass = {55Q10},
mrnumber = {0556925},
mrreviewer = {Donald M. Davis},
doi = {10.1017/S0305004100056887},
url = {https://doi.org/10.1017/S0305004100056887},
zblnumber = {0455.55007},
} -
[liulevicius] A. Liulevicius, "Zeroes of the cohomology of the Steenrod algebra," Proc. Amer. Math. Soc., vol. 14, pp. 972-976, 1963.
@ARTICLE{liulevicius,
author = {Liulevicius, Arunas},
title = {Zeroes of the cohomology of the {S}teenrod algebra},
journal = {Proc. Amer. Math. Soc.},
fjournal = {Proceedings of the American Mathematical Society},
volume = {14},
year = {1963},
pages = {972--976},
issn = {0002-9939},
mrclass = {55.34},
mrnumber = {0157383},
mrreviewer = {J. F. Adams},
doi = {10.2307/2035037},
url = {https://doi.org/10.2307/2035037},
zblnumber = {0148.17102},
} -
[sverre-thesis] S. Lunøe-Nielsen, The Segal conjecture for topological Hochschild homology of commutative $S$-algebras, 2005.
@MISC{sverre-thesis,
author = {Lunøe-Nielsen, Sverre},
title = {The {S}egal conjecture for topological {H}ochschild homology of commutative {$S$}-algebras},
year = {2005},
url = {http://urn.nb.no/URN:NBN:no-98057},
} -
[lunoenielsen-rognes] S. Lunøe-Nielsen and J. Rognes, "The Segal conjecture for topological Hochschild homology of complex cobordism," J. Topol., vol. 4, iss. 3, pp. 591-622, 2011.
@ARTICLE{lunoenielsen-rognes,
author = {Lunøe-Nielsen, Sverre and Rognes, John},
title = {The {S}egal conjecture for topological {H}ochschild homology of complex cobordism},
journal = {J. Topol.},
fjournal = {Journal of Topology},
volume = {4},
year = {2011},
number = {3},
pages = {591--622},
issn = {1753-8416},
mrclass = {55P91 (55N22 55P43 55S10)},
mrnumber = {2832570},
mrreviewer = {Birgit Richter},
doi = {10.1112/jtopol/jtr015},
url = {https://doi.org/10.1112/jtopol/jtr015},
zblnumber = {1229.55006},
} -
[rotation] J. Lurie, Rotation invariance in algebraic $K$-theory, 2015.
@MISC{rotation,
author = {Lurie, J.},
title = {Rotation invariance in algebraic {$K$}-theory},
year = {2015},
note= {available on author's webpage},
zblnumber = {},
} -
[ha] J. Lurie, Higher algebra, 2017.
@MISC{ha,
author = {Lurie, J.},
title = {Higher algebra},
year = {2017},
note= {available on author's webpage},
zblnumber = {},
} -
[sag] J. Lurie, Spectral Algebraic Geometry, 2018.
@MISC{sag,
author = {Lurie, J.},
title = {Spectral Algebraic Geometry},
year = {2018},
note= {available on author's webpage},
zblnumber = {},
} -
[mahowald-rezk] M. Mahowald and C. Rezk, "Brown-Comenetz duality and the Adams spectral sequence," Amer. J. Math., vol. 121, iss. 6, pp. 1153-1177, 1999.
@ARTICLE{mahowald-rezk,
author = {Mahowald, Mark and Rezk, Charles},
title = {Brown-{C}omenetz duality and the {A}dams spectral sequence},
journal = {Amer. J. Math.},
fjournal = {American Journal of Mathematics},
volume = {121},
year = {1999},
number = {6},
pages = {1153--1177},
issn = {0002-9327},
mrclass = {55P42 (55N22 55P60 55S10 55T15)},
mrnumber = {1719751},
mrreviewer = {J. P. C. Greenlees},
doi = {10.1353/ajm.1999.0043},
url = {https://doi.org/10.1353/ajm.1999.0043},
zblnumber = {0942.55012},
} -
[mathew-nilpotence] A. Mathew, "Examples of descent up to nilpotence," in Geometric and Topological Aspects of the Representation Theory of Finite Groups, Springer, Cham, 2018, vol. 242, pp. 269-311.
@INCOLLECTION{mathew-nilpotence,
author = {Mathew, Akhil},
title = {Examples of descent up to nilpotence},
booktitle = {Geometric and {T}opological {A}spects of the {R}epresentation {T}heory of {F}inite {G}roups},
series = {Springer Proc. Math. Stat.},
volume = {242},
pages = {269--311},
publisher = {Springer, Cham},
year = {2018},
mrclass = {18G80},
mrnumber = {3901164},
mrreviewer = {Paul Balmer},
doi = {10.1007/978-3-319-94033-5_11},
url = {https://doi.org/10.1007/978-3-319-94033-5_11},
zblnumber = {},
} -
[akhil-tr] A. Mathew, "On $K(1)$-local TR," Compos. Math., vol. 157, iss. 5, pp. 1079-1119, 2021.
@ARTICLE{akhil-tr,
author = {Mathew, Akhil},
title = {On {$K(1)$}-local {TR}},
journal = {Compos. Math.},
fjournal = {Compositio Mathematica},
volume = {157},
year = {2021},
number = {5},
pages = {1079--1119},
issn = {0010-437X},
mrclass = {19D55 (55P42)},
mrnumber = {4256236},
doi = {10.1112/S0010437X21007144},
url = {https://doi.org/10.1112/S0010437X21007144},
zblnumber = {1471.19002},
} -
[may-nilpotence] A. Mathew, N. Naumann, and J. Noel, "On a nilpotence conjecture of J. P. May," J. Topol., vol. 8, iss. 4, pp. 917-932, 2015.
@ARTICLE{may-nilpotence,
author = {Mathew, Akhil and Naumann, Niko and Noel, Justin},
title = {On a nilpotence conjecture of {J}. {P}. {M}ay},
journal = {J. Topol.},
fjournal = {Journal of Topology},
volume = {8},
year = {2015},
number = {4},
pages = {917--932},
issn = {1753-8416},
mrclass = {55P43 (55N22 55T15)},
mrnumber = {3431664},
mrreviewer = {William Cole Abram},
doi = {10.1112/jtopol/jtv021},
url = {https://doi.org/10.1112/jtopol/jtv021},
zblnumber = {1335.55009},
} -
[mathew-naumann-noel] A. Mathew, N. Naumann, and J. Noel, "Nilpotence and descent in equivariant stable homotopy theory," Adv. Math., vol. 305, pp. 994-1084, 2017.
@ARTICLE{mathew-naumann-noel,
author = {Mathew, Akhil and Naumann, Niko and Noel, Justin},
title = {Nilpotence and descent in equivariant stable homotopy theory},
journal = {Adv. Math.},
fjournal = {Advances in Mathematics},
volume = {305},
year = {2017},
pages = {994--1084},
issn = {0001-8708},
mrclass = {55P91 (55P42)},
mrnumber = {3570153},
mrreviewer = {Gregory Z. Arone},
doi = {10.1016/j.aim.2016.09.027},
url = {https://doi.org/10.1016/j.aim.2016.09.027},
zblnumber = {1420.55024},
} -
[mayproblems] J. P. May, "Problems in infinite loop space theory," in Conference on Homotopy Theory (Evanston, Ill., 1974), Soc. Mat. Mexicana, México, 1975, vol. 1, pp. 111-125.
@INCOLLECTION{mayproblems,
author = {May, J. P.},
title = {Problems in infinite loop space theory},
booktitle = {Conference on {H}omotopy {T}heory ({E}vanston, {I}ll., 1974)},
series = {Notas Mat. Simpos.},
volume = {1},
pages = {111--125},
publisher = {Soc. Mat. Mexicana, México},
year = {1975},
mrclass = {55P47},
mrnumber = {0761724},
zblnumber = {0332.55007},
} -
[miller-wilkerson] H. Miller and C. Wilkerson, "Vanishing lines for modules over the Steenrod algebra," J. Pure Appl. Algebra, vol. 22, iss. 3, pp. 293-307, 1981.
@ARTICLE{miller-wilkerson,
author = {Miller, Haynes and Wilkerson, Clarence},
title = {Vanishing lines for modules over the {S}teenrod algebra},
journal = {J. Pure Appl. Algebra},
fjournal = {Journal of Pure and Applied Algebra},
volume = {22},
year = {1981},
number = {3},
pages = {293--307},
issn = {0022-4049},
mrclass = {55S10 (16A24)},
mrnumber = {0629336},
mrreviewer = {Harvey Margolis},
doi = {10.1016/0022-4049(81)90104-3},
url = {https://doi.org/10.1016/0022-4049(81)90104-3},
zblnumber = {0469.55012},
} -
[milnor] J. Milnor, "The Steenrod algebra and its dual," Ann. of Math. (2), vol. 67, pp. 150-171, 1958.
@ARTICLE{milnor,
author = {Milnor, John},
title = {The {S}teenrod algebra and its dual},
journal = {Ann. of Math. (2)},
fjournal = {Annals of Mathematics. Second Series},
volume = {67},
year = {1958},
pages = {150--171},
issn = {0003-486X},
mrclass = {55.00 (18.00)},
mrnumber = {0099653},
mrreviewer = {G. Hirsch},
doi = {10.2307/1969932},
url = {https://doi.org/10.2307/1969932},
zblnumber = {0080.38003},
} -
[Mitchell] S. A. Mitchell, "The Morava $K$-theory of algebraic $K$-theory spectra," $K$-Theory, vol. 3, iss. 6, pp. 607-626, 1990.
@ARTICLE{Mitchell,
author = {Mitchell, S. A.},
title = {The {M}orava {$K$}-theory of algebraic {$K$}-theory spectra},
journal = {$K$-Theory},
fjournal = {$K$-Theory. An Interdisciplinary Journal for the Development, Application, and Influence of $K$-Theory in the Mathematical Sciences},
volume = {3},
year = {1990},
number = {6},
pages = {607--626},
issn = {0920-3036},
mrclass = {55N20 (19M05 55Q50)},
mrnumber = {1071898},
mrreviewer = {Roland Schwänzl},
doi = {10.1007/BF01054453},
url = {https://doi.org/10.1007/BF01054453},
zblnumber = {0709.55011},
} -
[moravaforms] J. Morava, "Forms of $K$-theory," Math. Z., vol. 201, iss. 3, pp. 401-428, 1989.
@ARTICLE{moravaforms,
author = {Morava, Jack},
title = {Forms of {$K$}-theory},
journal = {Math. Z.},
fjournal = {Mathematische Zeitschrift},
volume = {201},
year = {1989},
number = {3},
pages = {401--428},
issn = {0025-5874},
mrclass = {55N22 (11S31)},
mrnumber = {0999737},
mrreviewer = {P. S. Landweber},
doi = {10.1007/BF01214905},
url = {https://doi.org/10.1007/BF01214905},
zblnumber = {0709.55003},
} -
[Nave] L. S. Nave, "The Smith-Toda complex $V((p+1)/2)$ does not exist," Ann. of Math. (2), vol. 171, iss. 1, pp. 491-509, 2010.
-
[nikolaus-scholze] T. Nikolaus and P. Scholze, "On topological cyclic homology," Acta Math., vol. 221, iss. 2, pp. 203-409, 2018.
@ARTICLE{nikolaus-scholze,
author = {Nikolaus, Thomas and Scholze, Peter},
title = {On topological cyclic homology},
journal = {Acta Math.},
fjournal = {Acta Mathematica},
volume = {221},
year = {2018},
number = {2},
pages = {203--409},
issn = {0001-5962},
mrclass = {55U35 (16E40 18E30 19D99)},
mrnumber = {3904731},
mrreviewer = {Geoffrey M. L. Powell},
doi = {10.4310/ACTA.2018.v221.n2.a1},
url = {https://doi.org/10.4310/ACTA.2018.v221.n2.a1},
zblnumber = {1457.19007},
} -
[quillen-fgl] D. Quillen, "On the formal group laws of unoriented and complex cobordism theory," Bull. Amer. Math. Soc., vol. 75, pp. 1293-1298, 1969.
@ARTICLE{quillen-fgl,
author = {Quillen, Daniel},
title = {On the formal group laws of unoriented and complex cobordism theory},
journal = {Bull. Amer. Math. Soc.},
fjournal = {Bulletin of the American Mathematical Society},
volume = {75},
year = {1969},
pages = {1293--1298},
issn = {0002-9904},
mrclass = {57.10},
mrnumber = {0253350},
mrreviewer = {R. E. Stong},
doi = {10.1090/S0002-9904-1969-12401-8},
url = {https://doi.org/10.1090/S0002-9904-1969-12401-8},
zblnumber = {0199.26705},
} -
[quillen] D. Quillen, "Higher algebraic $\mathrm{K}$-theory," in Proceedings of the International Congress of Mathematicians, Vol. 1, 1975, pp. 171-176.
@INPROCEEDINGS{quillen,
author = {Quillen, Daniel},
title = {Higher algebraic {$\mathrm{K}$}-theory},
booktitle = {Proceedings of the {I}nternational {C}ongress of {M}athematicians, {V}ol. 1},
venue = {{V}ancouver, {B}. {C}., 1974},
pages = {171--176},
year = {1975},
mrclass = {18F25},
mrnumber = {0422392},
mrreviewer = {M. J. Dunwoody},
zblnumber = {0359.18014},
} -
[ravenel] D. C. Ravenel, Complex Cobordism and Stable Homotopy Groups of Spheres, Academic Press, Inc., Orlando, FL, 1986, vol. 121.
@BOOK{ravenel,
author = {Ravenel, Douglas C.},
title = {Complex Cobordism and Stable Homotopy Groups of Spheres},
series = {Pure Appl. Math.},
volume = {121},
publisher = {Academic Press, Inc., Orlando, FL},
year = {1986},
pages = {xx+413},
isbn = {0-12-583430-6; 0-12-583431-4},
mrclass = {55-02 (55Qxx 57-02)},
mrnumber = {0860042},
mrreviewer = {Joseph Neisendorfer},
zblnumber = {0608.55001},
} -
[smith] D. C. Ravenel, Nilpotence and Periodicity in Stable Homotopy Theory, Princeton Univ. Press, Princeton, NJ, 1992, vol. 128.
@BOOK{smith,
author = {Ravenel, Douglas C.},
title = {Nilpotence and {P}eriodicity in {S}table {H}omotopy {T}heory},
series = {Annals of Mathematics Studies},
volume = {128},
note = {Appendix C by Jeff Smith},
publisher = {Princeton Univ. Press, Princeton, NJ},
year = {1992},
pages = {xiv+209},
isbn = {0-691-02572-X},
mrclass = {55P42 (55N22 55Q10 57R77)},
mrnumber = {1192553},
mrreviewer = {N. J. Kuhn},
doi = {10.1515/9781400882489},
url = {https://doi.org/10.1515/9781400882489},
zblnumber = {0774.55001},
} -
[richterstage] B. Richter, "A lower bound for coherences on the Brown-Peterson spectrum," Algebr. Geom. Topol., vol. 6, pp. 287-308, 2006.
@ARTICLE{richterstage,
author = {Richter, Birgit},
title = {A lower bound for coherences on the {B}rown-{P}eterson spectrum},
journal = {Algebr. Geom. Topol.},
fjournal = {Algebraic \& Geometric Topology},
volume = {6},
year = {2006},
pages = {287--308},
issn = {1472-2747},
mrclass = {55P43 (13D03)},
mrnumber = {2199461},
mrreviewer = {Andrey Yu. Lazarev},
doi = {10.2140/agt.2006.6.287},
url = {https://doi.org/10.2140/agt.2006.6.287},
zblnumber = {1095.55005},
} -
[rognes-2adicZ] J. Rognes, "Algebraic $K$-theory of the two-adic integers," J. Pure Appl. Algebra, vol. 134, iss. 3, pp. 287-326, 1999.
@ARTICLE{rognes-2adicZ,
author = {Rognes, John},
title = {Algebraic {$K$}-theory of the two-adic integers},
journal = {J. Pure Appl. Algebra},
fjournal = {Journal of Pure and Applied Algebra},
volume = {134},
year = {1999},
number = {3},
pages = {287--326},
issn = {0022-4049},
mrclass = {19D55 (55P42 55Q52)},
mrnumber = {1663391},
mrreviewer = {Jerry Lodder},
doi = {10.1016/S0022-4049(97)00156-4},
url = {https://doi.org/10.1016/S0022-4049(97)00156-4},
zblnumber = {0929.19004},
} -
[rognes-oberwolfach] J. Rognes, Algebraic K-theory of finitely presented ring spectra, 2000.
@MISC{rognes-oberwolfach,
author = {Rognes, John},
title = {Algebraic {K}-theory of finitely presented ring spectra},
year = {2000},
note = {Available on author's webpage},
zblnumber = {},
} -
[rognesmsri] J. Rognes, Chromatic redshift, 2014.
@MISC{rognesmsri,
author = {Rognes, John},
title = {Chromatic redshift},
year = {2014},
arxiv = {1403.4838},
zblnumber = {},
} -
[sengerBP] A. Senger, The Brown-Peterson spectrum is not ${E}_{2(p^2+2)}$ at odd primes, 2022.
@MISC{sengerBP,
author = {Senger, A.},
title = {The {B}rown-{P}eterson spectrum is not ${E}_{2(p^2+2)}$ at odd primes},
year = {2022},
arxiv = {1710.09822},
zblnumber = {},
} -
[strickland] N. P. Strickland, "Products on $MU$-modules," Trans. Amer. Math. Soc., vol. 351, iss. 7, pp. 2569-2606, 1999.
@ARTICLE{strickland,
author = {Strickland, N. P.},
title = {Products on {$MU$}-modules},
journal = {Trans. Amer. Math. Soc.},
fjournal = {Transactions of the American Mathematical Society},
volume = {351},
year = {1999},
number = {7},
pages = {2569--2606},
issn = {0002-9947},
mrclass = {55N22 (55N20)},
mrnumber = {1641115},
mrreviewer = {W. Stephen Wilson},
doi = {10.1090/S0002-9947-99-02436-8},
url = {https://doi.org/10.1090/S0002-9947-99-02436-8},
zblnumber = {0924.55005},
} -
[thomason] R. W. Thomason, "The Lichtenbaum-Quillen conjecture for $K/\ell_\ast[\beta^{-1}]$," in Current Trends in Algebraic Topology, Part 1 (London, Ont., 1981), Amer. Math. Soc., Providence, R.I., 1982, vol. 2, pp. 117-139.
@INCOLLECTION{thomason,
author = {Thomason, R. W.},
title = {The {L}ichtenbaum-{Q}uillen conjecture for {$K/\ell_\ast[\beta^{-1}]$}},
booktitle = {Current {T}rends in {A}lgebraic {T}opology, {P}art 1 ({L}ondon, {O}nt., 1981)},
series = {CMS Conf. Proc.},
volume = {2},
pages = {117--139},
publisher = {Amer. Math. Soc., Providence, R.I.},
year = {1982},
mrclass = {18F25 (12A70 14F15)},
mrnumber = {0686114},
mrreviewer = {Daniel R. Grayson},
zblnumber = {0563.14009},
} -
[tilson] S. Tilson, Power operations in the Künneth spectral sequence and commutative $\mathrm{H}\mathbb{F}_p$-algebras, 2018.
@MISC{tilson,
author = {Tilson, S.},
title = {Power operations in the {K}{ü}nneth spectral sequence and commutative {$\mathrm{H}\mathbb{F}_p$}-algebras},
year = {2018},
arxiv = {1602.06736},
} -
[veen] T. Veen, "Detecting periodic elements in higher topological Hochschild homology," Geom. Topol., vol. 22, iss. 2, pp. 693-756, 2018.
@ARTICLE{veen,
author = {Veen, Torleif},
title = {Detecting periodic elements in higher topological {H}ochschild homology},
journal = {Geom. Topol.},
fjournal = {Geometry \& Topology},
volume = {22},
year = {2018},
number = {2},
pages = {693--756},
issn = {1465-3060},
mrclass = {55P42 (55P91)},
mrnumber = {3748678},
mrreviewer = {Marco Varisco},
doi = {10.2140/gt.2018.22.693},
url = {https://doi.org/10.2140/gt.2018.22.693},
zblnumber = {1384.55007},
} -
[voeI] V. Voevodsky, "Motivic cohomology with ${\bf Z}/2$-coefficients," Publ. Math. Inst. Hautes Études Sci., iss. 98, pp. 59-104, 2003.
@ARTICLE{voeI,
author = {Voevodsky, Vladimir},
title = {Motivic cohomology with {${\bf Z}/2$}-coefficients},
journal = {Publ. Math. Inst. Hautes \'{E}tudes Sci.},
fjournal = {Publications Mathématiques. Institut de Hautes \'{E}tudes Scientifiques},
number = {98},
year = {2003},
pages = {59--104},
issn = {0073-8301},
mrclass = {14F42 (12G05 19D45 19E15)},
mrnumber = {2031199},
mrreviewer = {Eric M. Friedlander},
doi = {10.1007/s10240-003-0010-6},
url = {https://doi.org/10.1007/s10240-003-0010-6},
zblnumber = {1057.14028},
} -
[voeII] V. Voevodsky, "On motivic cohomology with $\Bbb Z/l$-coefficients," Ann. of Math. (2), vol. 174, iss. 1, pp. 401-438, 2011.
@ARTICLE{voeII,
author = {Voevodsky, Vladimir},
title = {On motivic cohomology with {$\bold Z/l$}-coefficients},
journal = {Ann. of Math. (2)},
fjournal = {Annals of Mathematics. Second Series},
volume = {174},
year = {2011},
number = {1},
pages = {401--438},
issn = {0003-486X},
mrclass = {14F42 (19D45)},
mrnumber = {2811603},
mrreviewer = {Matthias Wendt},
doi = {10.4007/annals.2011.174.1.11},
url = {https://doi.org/10.4007/annals.2011.174.1.11},
zblnumber = {1236.14026},
} -
[waldhausen] F. Waldhausen, "Algebraic $\mathrm{K}$-theory of spaces, localization, and the chromatic filtration of stable homotopy," in Algebraic Topology, Springer, Berlin, 1984, vol. 1051, pp. 173-195.
@INCOLLECTION{waldhausen,
author = {Waldhausen, Friedhelm},
title = {Algebraic {$\mathrm{K}$}-theory of spaces, localization, and the chromatic filtration of stable homotopy},
booktitle = {Algebraic Topology},
venue = {{A}arhus, 1982},
series = {Lecture Notes in Math.},
volume = {1051},
pages = {173--195},
publisher = {Springer, Berlin},
year = {1984},
mrclass = {57N37 (18F25 19D10)},
mrnumber = {0764579},
mrreviewer = {V. P. Snaith},
doi = {10.1007/BFb0075567},
url = {https://doi.org/10.1007/BFb0075567},
zblnumber = {0562.55002},
} -
[westerland] C. Westerland, "A higher chromatic analogue of the image of $J$," Geom. Topol., vol. 21, iss. 2, pp. 1033-1093, 2017.
@ARTICLE{westerland,
author = {Westerland, Craig},
title = {A higher chromatic analogue of the image of {$J$}},
journal = {Geom. Topol.},
fjournal = {Geometry \& Topology},
volume = {21},
year = {2017},
number = {2},
pages = {1033--1093},
issn = {1465-3060},
mrclass = {55P42 (19L20 55N15 55P20 55Q51)},
mrnumber = {3626597},
mrreviewer = {Markus Szymik},
doi = {10.2140/gt.2017.21.1033},
url = {https://doi.org/10.2140/gt.2017.21.1033},
zblnumber = {1371.19003},
} -
[wilson] S. W. Wilson, "The $\Omega $-spectrum for Brown-Peterson cohomology. II," Amer. J. Math., vol. 97, pp. 101-123, 1975.
@ARTICLE{wilson,
author = {Wilson, W. Stephen},
title = {The {$\Omega $}-spectrum for {B}rown-{P}eterson cohomology. {II}},
journal = {Amer. J. Math.},
fjournal = {American Journal of Mathematics},
volume = {97},
year = {1975},
pages = {101--123},
issn = {0002-9327},
mrclass = {55B20},
mrnumber = {0383390},
mrreviewer = {J. W. Vick},
doi = {10.2307/2373662},
url = {https://doi.org/10.2307/2373662},
zblnumber = {0303.55003},
}
Full Article