Abstract
The goal of this paper is to show that the cohomology of compact unitary Shimura varieties is concentrated in the middle degree and torsion-free, after localizing at a maximal ideal of the Hecke algebra satisfying a suitable genericity assumption. Along the way, we establish various foundational results on the geometry of the Hodge-Tate period map. In particular, we compare the fibres of the Hodge-Tate period map with Igusa varieties.
-
[calegari-geraghty] F. Calegari and D. Geraghty, Modularity lifting beyond the Taylor-Wiles method.
@misc{calegari-geraghty,
author = {Calegari, Frank and Geraghty, David},
TITLE = {Modularity lifting beyond the {T}aylor-{W}iles method},
ARXIV = {1207.4224},
} -
[boyer]
P. Boyer, "Sur la torsion dans la cohomologie des variétés de Shimura de Kottwitz-Harris-Taylor," J. Inst. Math. Jussieu, p. 19, 2017.
@article{boyer,
author = {Boyer, Pascal},
TITLE = {{S}ur la torsion dans la cohomologie des variétés de {S}himura de {K}ottwitz-{H}arris-{T}aylor},
journal = {J. Inst. Math. Jussieu},
fjournal = {Journal of the Institute of Mathematics of Jussieu},
publisher = {Cambridge University Press},
address = {Cambridge},
doi = {10.1017/S1474748017000093},
note = {published online 30 March 2017},
YEAR = {2017},
PAGES = {19 pp.},
} -
[scholzesurvey]
P. Scholze, "Perfectoid spaces: A survey," in Current Developments in Mathematics 2012, Int. Press, Somerville, MA, 2013, pp. 193-227.
@incollection{scholzesurvey,
author = {Scholze, Peter},
TITLE = {Perfectoid spaces: {A} survey},
BOOKTITLE = {Current Developments in Mathematics 2012},
PAGES = {193--227},
PUBLISHER = {Int. Press, Somerville, MA},
YEAR = {2013},
MRCLASS = {14G22 (14C30 14G20 14L05)},
MRNUMBER = {3204346},
MRREVIEWER = {Lei Fu},
DOI = {10.4310/CDM.2012.v2012.n1.a4},
ZBLNUMBER = {06302780},
} -
[bhattscholzeperf]
B. Bhatt and P. Scholze, "Projectivity of the Witt vector affine Grassmannian," Invent. Math., vol. 209, iss. 2, pp. 329-423, 2017.
@ARTICLE{bhattscholzeperf,
author = {Bhatt, Bhargav and Scholze, Peter},
TITLE = {Projectivity of the {W}itt vector affine {G}rassmannian},
JOURNAL = {Invent. Math.},
FJOURNAL = {Inventions Mathematicae},
year = {2017},
volume = {209},
number = {2},
pages = {329--423},
DOI = {10.1007/s00222-016-0710-4},
} -
[shin-igusa]
S. W. Shin, "Counting points on Igusa varieties," Duke Math. J., vol. 146, iss. 3, pp. 509-568, 2009.
@article {shin-igusa,
author = {Shin, Sug Woo},
TITLE = {Counting points on {I}gusa varieties},
JOURNAL = {Duke Math. J.},
FJOURNAL = {Duke Mathematical Journal},
VOLUME = {146},
YEAR = {2009},
NUMBER = {3},
PAGES = {509--568},
ISSN = {0012-7094},
CODEN = {DUMJAO},
MRCLASS = {11G18 (11F72 11G15 11R39 14G35)},
MRNUMBER = {2484281},
MRREVIEWER = {Nguy{\cftil{e}}n Qu{ô}c Th{á}ng},
DOI = {10.1215/00127094-2009-004},
URL = {http://dx.doi.org/10.1215/00127094-2009-004},
ZBLNUMBER = {1218.11061},
} -
[shin-stable]
S. W. Shin, "A stable trace formula for Igusa varieties," J. Inst. Math. Jussieu, vol. 9, iss. 4, pp. 847-895, 2010.
@article {shin-stable,
author = {Shin, Sug Woo},
TITLE = {A stable trace formula for {I}gusa varieties},
JOURNAL = {J. Inst. Math. Jussieu},
FJOURNAL = {Journal of the Institute of Mathematics of Jussieu. JIMJ. Journal de l'Institut de Mathématiques de Jussieu},
VOLUME = {9},
YEAR = {2010},
NUMBER = {4},
PAGES = {847--895},
ISSN = {1474-7480},
MRCLASS = {11G18 (11F72 11G15 11R39 22E55)},
MRNUMBER = {2684263},
MRREVIEWER = {Nguy{\cftil{e}}n Qu{ô}c Th{á}ng},
DOI = {10.1017/S1474748010000046},
URL = {http://dx.doi.org/10.1017/S1474748010000046},
ZBLNUMBER = {1206.22011},
} -
[scholze-letter-dat] P. Scholze, Letter to Jean-Francois Dat, April 28, 2011.
@misc{scholze-letter-dat,
author = {Scholze, Peter},
TITLE = {{L}etter to {J}ean-{F}rancois {D}at},
YEAR = {April 28, 2011},
sortyear={2011},
} -
[scholzerigid]
P. Scholze, "$p$-adic Hodge theory for rigid-analytic varieties," Forum Math. Pi, vol. 1, p. 1, 2013.
@article {scholzerigid,
author = {Scholze, Peter},
TITLE = {{$p$}-adic {H}odge theory for rigid-analytic varieties},
JOURNAL = {Forum Math. Pi},
FJOURNAL = {Forum of Mathematics. Pi},
VOLUME = {1},
YEAR = {2013},
PAGES = {e1, 77},
ISSN = {2050-5086},
MRCLASS = {14G22 (14C30 14F30 14G20 32J27 32P05)},
MRNUMBER = {3090230},
MRREVIEWER = {Hui June Zhu},
DOI = {10.1017/fmp.2013.1},
URL = {http://dx.doi.org/10.1017/fmp.2013.1},
zblnumber = {1297.14023},
} -
[farguesGbun] L. Fargues, $G$-torseurs en théorie de Hodge $p$-adique, 2015.
@misc{farguesGbun,
author = {Fargues, Laurent},
TITLE = {{$G$}-torseurs en théorie de {H}odge {$p$}-adique},
YEAR = {2015},
} -
[scholzelectures] J. Weinstein, Peter Scholze’s Lectures on $p$-adic geometry, 2014.
@misc{scholzelectures,
author = {Weinstein, Jared},
TITLE = {Peter {S}cholze's Lectures on {$p$}-adic geometry},
YEAR = {2014},
} -
[fargues-geom-langlands] L. Fargues, Geometrization of the local Langlands correspondence: an overview, 2016.
@misc{fargues-geom-langlands,
author = {Fargues, Laurent},
title = {Geometrization of the local Langlands correspondence: an overview},
ARXIV = {1602.00999},
year ={ 2016},
} -
[DeligneVarSh] P. Deligne, "Travaux de Shimura," in Séminaire Bourbaki, 23ème Année (1970/71), Exp. No. 389, Springer, Berlin, 1971, vol. 244, pp. 123-165.
@incollection {DeligneVarSh,
author = {Deligne, Pierre},
TITLE = {Travaux de {S}himura},
BOOKTITLE = {Séminaire {B}ourbaki, 23ème Année (1970/71), {E}xp. {N}o. 389},
PAGES = {123--165},
SERIES={Lecture Notes in Math.},
VOLUME={244},
PUBLISHER = {Springer, Berlin},
YEAR = {1971},
MRCLASS = {14G25 (10D25 14K15)},
MRNUMBER = {0498581},
MRREVIEWER = {Author's review},
ZBLNUMBER = {0225.14007},
} -
[ngopolo] B. C. Ngô and P. Polo, "Résolutions de Demazure affines et formule de Casselman-Shalika géométrique," J. Algebraic Geom., vol. 10, iss. 3, pp. 515-547, 2001.
@article {ngopolo,
author = {Ng{ô},
Bao Ch{\^{a}}u and Polo, P.},
TITLE = {Résolutions de {D}emazure affines et formule de {C}asselman-{S}halika géométrique},
JOURNAL = {J. Algebraic Geom.},
FJOURNAL = {Journal of Algebraic Geometry},
VOLUME = {10},
YEAR = {2001},
NUMBER = {3},
PAGES = {515--547},
ISSN = {1056-3911},
MRCLASS = {14F43 (14F17)},
MRNUMBER = {1832331},
MRREVIEWER = {Nguy{\cftil{e}}n Qu{ô}c Th{á}ng},
ZBLNUMBER = {1041.14002},
} -
[rapoportappendix] M. Rapoport, Accessible and weakly accessible period domains, 2015.
@misc{rapoportappendix,
author = {Rapoport, Michael},
TITLE = {Accessible and weakly accessible period domains},
NOTE = {Appendix A to \arxiv{1506.04022}},
YEAR = {2015},
} -
[bhattscholze] B. Bhatt and P. Scholze, "The pro-étale topology for schemes," in De la Géométrie Algébrique aux Formes Automorphes (I), Paris: Math. Soc. France, 2015, vol. 369, pp. 99-201.
@incollection{bhattscholze,
author = {Bhatt, Bhargav and Scholze, Peter},
TITLE = {The pro-étale topology for schemes},
BOOKTITLE={De la Géométrie Algébrique aux Formes Automorphes (I)},
SERIES = {Astérisque},
PUBLISHER={Math. Soc. France},
ADDRESS = {Paris},
VOLUME={369},
YEAR = {2015},
PAGES = {99--201},
MRNUMBER = {3379634},
ZBLNUMBER = {1351.19001},
} -
[labesse] J. Labesse, Cohomologie, Stabilisation et Changement de Base, Math. Soc. France, Paris, 1999, vol. 257.
@book{labesse,
author = {Labesse, Jean-Pierre},
TITLE = {Cohomologie, Stabilisation et Changement de Base},
NOTE = {appendix A by Laurent Clozel and Labesse, and Appendix B by Lawrence Breen},
SERIES = {Astérisque},
PUBLISHER={Math. Soc. France, Paris},
VOLUME= {257},
YEAR = {1999},
PAGES = {vi+161},
ISSN = {0303-1179},
MRCLASS = {22E55 (11F70 18G30)},
MRNUMBER = {1695940},
MRREVIEWER = {Nguy{\cftil{e}}n Qu{ô}c Th{á}ng},
ZBLNUMBER = {1024.11034},
} -
[shin-rapoport-zink]
S. W. Shin, "On the cohomology of Rapoport-Zink spaces of EL-type," Amer. J. Math., vol. 134, iss. 2, pp. 407-452, 2012.
@article {shin-rapoport-zink,
author = {Shin, Sug Woo},
TITLE = {On the cohomology of {R}apoport-{Z}ink spaces of {EL}-type},
JOURNAL = {Amer. J. Math.},
FJOURNAL = {American Journal of Mathematics},
VOLUME = {134},
YEAR = {2012},
NUMBER = {2},
PAGES = {407--452},
ISSN = {0002-9327},
CODEN = {AJMAAN},
MRCLASS = {11G15 (11F72 14F30 14G35 14L15)},
MRNUMBER = {2905002},
MRREVIEWER = {Nguy{\cftil{e}}n Qu{ô}c Th{á}ng},
DOI = {10.1353/ajm.2012.0009},
URL = {http://dx.doi.org/10.1353/ajm.2012.0009},
ZBLNUMBER = {1245.14028},
} -
[arthura]
J. Arthur, "The invariant trace formula. I. Local theory," J. Amer. Math. Soc., vol. 1, iss. 2, pp. 323-383, 1988.
@ARTICLE{arthura,
author = {Arthur, James},
title = {The invariant trace formula. {I}. {L}ocal theory},
journal = {J. Amer. Math. Soc.},
fjournal = {Journal of the American Mathematical Society},
volume = {1},
year = {1988},
number = {2},
pages = {323--383},
issn = {0894-0347},
mrclass = {22E55 (11F70 11F72)},
mrnumber = {0928262},
mrreviewer = {A. B. Venkov},
doi = {10.2307/1990920},
url = {http://dx.doi.org/10.2307/1990920},
zblnumber = {0682.10021},
} -
[arthurb]
J. Arthur, "The invariant trace formula. II. Global theory," J. Amer. Math. Soc., vol. 1, iss. 3, pp. 501-554, 1988.
@ARTICLE{arthurb,
author = {Arthur, James},
title = {The invariant trace formula. {II}. {G}lobal theory},
journal = {J. Amer. Math. Soc.},
fjournal = {Journal of the American Mathematical Society},
volume = {1},
year = {1988},
number = {3},
pages = {501--554},
issn = {0894-0347},
mrclass = {22E55 (11F72)},
mrnumber = {0939691},
mrreviewer = {A. B. Venkov},
doi = {10.2307/1990948},
url = {http://dx.doi.org/10.2307/1990948},
zblnumber = {0667.10019},
} -
[arthur-lefschetz]
J. Arthur, "The $L^2$-Lefschetz numbers of Hecke operators," Invent. Math., vol. 97, iss. 2, pp. 257-290, 1989.
@ARTICLE{arthur-lefschetz,
author = {Arthur, James},
title = {The {$L^2$}-{L}efschetz numbers of {H}ecke operators},
journal = {Invent. Math.},
fjournal = {Inventiones Mathematicae},
volume = {97},
year = {1989},
number = {2},
pages = {257--290},
issn = {0020-9910},
mrclass = {22E55},
mrnumber = {1001841},
mrreviewer = {Stephen Gelbart},
doi = {10.1007/BF01389042},
url = {http://dx.doi.org/10.1007/BF01389042},
zblnumber = {0692.22004},
} -
[arthur-endoscopic-classification]
J. Arthur, The Endoscopic Classification of Representations: Orthogonal and Symplectic Groups, American Mathematical Society, Providence, RI, 2013, vol. 61.
@BOOK{arthur-endoscopic-classification,
author = {Arthur, James},
title = {The {E}ndoscopic {C}lassification of {R}epresentations: {O}rthogonal and {S}ymplectic {G}roups},
series = {American Mathematical Society Colloquium Publications},
volume = {61},
publisher = {American Mathematical Society, Providence, RI},
year = {2013},
pages = {xviii+590},
isbn = {978-0-8218-4990-3},
mrclass = {22E55 (11F66 11F70 11F72 11R37 20G25 22E50)},
mrnumber = {3135650},
mrreviewer = {Dihua Jiang},
doi = {10.1090/coll/061},
url = {http://dx.doi.org/10.1090/coll/061},
zblnumber = {1310.22014},
} -
[badulescu]
A. I. Badulescu, "Jacquet-Langlands et unitarisabilité," J. Inst. Math. Jussieu, vol. 6, iss. 3, pp. 349-379, 2007.
@ARTICLE{badulescu,
author = {Badulescu, Alexandru Ioan},
title = {Jacquet-{L}anglands et unitarisabilité},
journal = {J. Inst. Math. Jussieu},
fjournal = {Journal of the Institute of Mathematics of Jussieu. JIMJ. Journal de l'Institut de Mathématiques de Jussieu},
volume = {6},
year = {2007},
number = {3},
pages = {349--379},
issn = {1474-7480},
mrclass = {20G05 (20G25)},
mrnumber = {2329758},
doi = {10.1017/S1474748007000035},
url = {http://dx.doi.org/10.1017/S1474748007000035},
zblnumber = {1159.22005},
} -
[bbm]
P. Berthelot, L. Breen, and W. Messing, Théorie de Dieudonné Cristalline II, Springer-Verlag, New York, 1982, vol. 930.
@BOOK{bbm,
author = {Berthelot, Pierre and Breen, Lawrence and Messing, William},
title = {Théorie de {D}ieudonné {C}ristalline {II}},
series = {Lecture Notes in Math.},
volume = {930},
publisher = {Springer-Verlag, New York},
year = {1982},
pages = {x+261},
isbn = {3-540-11556-0},
mrclass = {14L05 (14F30)},
mrnumber = {0667344},
mrreviewer = {Lucile BÂ\copyright{}gueri},
doi = {10.1007/BFb0093025},
zblnumber = {0516.14015},
} -
[berthelotvalparfait]
P. Berthelot, "Théorie de Dieudonné sur un anneau de valuation parfait," Ann. Sci. École Norm. Sup. (4), vol. 13, iss. 2, pp. 225-268, 1980.
@ARTICLE{berthelotvalparfait,
author = {Berthelot, Pierre},
title = {Théorie de {D}ieudonné sur un anneau de valuation parfait},
journal = {Ann. Sci. École Norm. Sup. (4)},
fjournal = {Annales Scientifiques de l'École Normale Supérieure. Quatrième Série},
volume = {13},
year = {1980},
number = {2},
pages = {225--268},
issn = {0012-9593},
mrclass = {14L05 (14F30 14G20)},
mrnumber = {0584086},
mrreviewer = {William E. Lang},
doi = {10.24033/asens.1381},
zblnumber = {0441.14012},
} -
[buzzardgee]
K. Buzzard and T. Gee, "The conjectural connections between automorphic representations and Galois representations," in Automorphic forms and Galois representations. Vol. 1, Cambridge Univ. Press, Cambridge, 2014, vol. 414, pp. 135-187.
@INCOLLECTION{buzzardgee,
author = {Buzzard, Kevin and Gee, Toby},
title = {The conjectural connections between automorphic representations and {G}alois representations},
booktitle = {Automorphic forms and {G}alois representations. {V}ol. 1},
series = {London Math. Soc. Lecture Note Ser.},
volume = {414},
pages = {135--187},
publisher = {Cambridge Univ. Press, Cambridge},
year = {2014},
mrclass = {11F33},
mrnumber = {3444225},
doi = {10.1017/CBO9781107446335.006},
url = {http://dx.doi.org/10.1017/CBO9781107446335.006},
zblnumber = {06589912},
} -
[blasius]
D. Blasius, "A $p$-adic property of Hodge classes on abelian varieties," in Motives (Seattle, WA, 1991), Amer. Math. Soc., Providence, RI, 1994, vol. 55, pp. 293-308.
@INCOLLECTION{blasius,
author = {Blasius, Don},
title = {A {$p$}-adic property of {H}odge classes on abelian varieties},
booktitle = {Motives ({S}eattle, {WA},
1991)},
series = {Proc. Sympos. Pure Math.},
volume = {55},
pages = {293--308},
publisher = {Amer. Math. Soc., Providence, RI},
year = {1994},
mrclass = {14F30 (11G10 14C30 14K99)},
mrnumber = {1265557},
mrreviewer = {Abdellah Mokrane},
zblnumber = {0821.14028},
doi = {10.1090/pspum/055.2/1265557},
} -
[borelwallach] A. Borel and N. R. Wallach, Continuous cohomology, discrete subgroups, and representations of reductive groups, Princeton Univ. Press, Princeton, NJ, 1980, vol. 94.
@BOOK{borelwallach,
author = {Borel, Armand and Wallach, Nolan R.},
title = {Continuous cohomology, discrete subgroups, and representations of reductive groups},
series = {Ann. of Math. Stud.},
volume = {94},
publisher = {Princeton Univ. Press, Princeton, NJ},
year = {1980},
pages = {xvii+388},
isbn = {0-691-08248-0; 0-691-08249-9},
mrclass = {22E41 (22E40 22E45 57T15)},
mrnumber = {0554917},
mrreviewer = {Roger Howe},
zblnumber = {0443.22010},
} -
[caraiani]
A. Caraiani, "Local-global compatibility and the action of monodromy on nearby cycles," Duke Math. J., vol. 161, iss. 12, pp. 2311-2413, 2012.
@ARTICLE{caraiani,
author = {Caraiani, Ana},
title = {Local-global compatibility and the action of monodromy on nearby cycles},
journal = {Duke Math. J.},
fjournal = {Duke Mathematical Journal},
volume = {161},
year = {2012},
number = {12},
pages = {2311--2413},
issn = {0012-7094},
mrclass = {22E57 (11F70 11F80 11R39 14G35)},
mrnumber = {2972460},
mrreviewer = {Kai-Wen Lan},
doi = {10.1215/00127094-1723706},
url = {http://dx.doi.org/10.1215/00127094-1723706},
zblnumber = {06095601},
} -
[chenevier-harris]
G. Chenevier and M. Harris, "Construction of automorphic Galois representations, II," Camb. J. Math., vol. 1, iss. 1, pp. 53-73, 2013.
@ARTICLE{chenevier-harris,
author = {Chenevier, Gaëtan and Harris, Michael},
title = {Construction of automorphic {G}alois representations, {II}},
journal = {Camb. J. Math.},
fjournal = {Cambridge Journal of Mathematics},
volume = {1},
year = {2013},
number = {1},
pages = {53--73},
issn = {2168-0930},
mrclass = {11F80},
mrnumber = {3272052},
mrreviewer = {Krzysztof Klosin},
doi = {10.4310/CJM.2013.v1.n1.a2},
url = {http://dx.doi.org/10.4310/CJM.2013.v1.n1.a2},
zblnumber = {1310.11062},
} -
[delignevb]
P. Deligne, Équations différentielles à points singuliers réguliers, Springer-Verlag, New York, 1970, vol. 163.
@BOOK{delignevb,
author = {Deligne, Pierre},
title = {Équations différentielles à points singuliers réguliers},
series = {Lecture Notes in Math.},
VOLUME={163},
publisher = {Springer-Verlag, New York},
year = {1970},
pages = {iii+133},
mrclass = {14D05 (14C30)},
mrnumber = {0417174},
mrreviewer = {Helmut Hamm},
zblnumber = {0244.14004},
doi = {10.1007/BFb0061194},
} -
@BOOK{SGA41/2,
author = {Deligne, Pierre},
title = {Cohomologie étale},
series = {Lecture Notes in Math.},
VOLUME={569},
note = {Séminaire de Géométrie Algébrique du Bois-Marie SGA 4${\frac{1}{2}}$, Avec la collaboration de J. F. Boutot, A. Grothendieck, L. Illusie et J. L. Verdier},
publisher = {Springer-Verlag, New York},
year = {1977},
pages = {iv+312pp},
mrclass = {14F20},
mrnumber = {0463174},
mrreviewer = {J. S. Milne},
zblnumber = {0345.00010},
doi = {10.1007/BFb0091516},
} -
[deligne-varietes] P. Deligne, "Variétés de Shimura: interprétation modulaire, et techniques de construction de modèles canoniques," in Automorphic Forms, Representations and $L$-Functions, Part 2, Amer. Math. Soc., Providence, RI, 1979, vol. XXXIII, pp. 247-289.
@INCOLLECTION{deligne-varietes,
author = {Deligne, Pierre},
title = {Variétés de {S}himura: interprétation modulaire, et techniques de construction de modèles canoniques},
booktitle = {Automorphic Forms, Representations and {$L$}-Functions, {P}art 2},
VENUE={{P}roc. {S}ympos. {P}ure {M}ath., {O}regon {S}tate {U}niv., {C}orvallis, {OR},
1977},
series = {Proc. Sympos. Pure Math.},
VOLUME={XXXIII},
pages = {247--289},
publisher = {Amer. Math. Soc., Providence, RI},
year = {1979},
mrclass = {10D20 (14D20 14G25 14K15)},
mrnumber = {0546620},
mrreviewer = {J. S. Milne},
zblnumber = {0437.14012},
} -
[delignehodge]
P. Deligne, J. S. Milne, A. Ogus, and K. Shih, Hodge Cycles, Motives, and Shimura Varieties, Springer-Verlag, New York, 1982, vol. 900.
@BOOK{delignehodge,
author = {Deligne, Pierre and Milne, James S. and Ogus, Arthur and Shih, Kuang-yen},
title = {Hodge {C}ycles, {M}otives, and {S}himura {V}arieties},
series = {Lecture Notes in Math.},
volume = {900},
publisher = {Springer-Verlag, New York},
year = {1982},
pages = {ii+414},
isbn = {3-540-11174-3},
mrclass = {14Kxx (10D25 12A67 14A20 14F30 14K22)},
mrnumber = {0654325},
zblnumber = {0465.00010},
doi = {10.1007/978-3-540-38955-2},
} -
[emerton-gee]
M. Emerton and T. Gee, "$p$-adic Hodge-theoretic properties of étale cohomology with ${ mod}\, p$ coefficients, and the cohomology of Shimura varieties," Algebra Number Theory, vol. 9, iss. 5, pp. 1035-1088, 2015.
@ARTICLE{emerton-gee,
author = {Emerton, Matthew and Gee, Toby},
title = {{$p$}-adic {H}odge-theoretic properties of étale cohomology with {${\rm mod}\, p$} coefficients, and the cohomology of {S}himura varieties},
journal = {Algebra Number Theory},
fjournal = {Algebra \& Number Theory},
volume = {9},
year = {2015},
number = {5},
pages = {1035--1088},
issn = {1937-0652},
mrclass = {11F33 (14Gxx)},
mrnumber = {3365999},
doi = {10.2140/ant.2015.9.1035},
url = {http://dx.doi.org/10.2140/ant.2015.9.1035},
zblnumber = {1321.11050},
} -
[fargues] L. Fargues, "Quelques résultats et conjectures concernant la courbe," in De la Géométrie Algébrique aux Formes Automorphes (I), Math. Soc. France, Paris, 2015, vol. 369, pp. 325-374.
@incollection{fargues,
author = {Fargues, Laurent},
title = {Quelques résultats et conjectures concernant la courbe},
booktitle={De la Géométrie Algébrique aux Formes Automorphes (I)},
NOTE={une collection d'articles en l'honneur du soixantime anniversaire de Gérard Laumon},
PUBLISHER={Math. Soc. France, Paris},
SERIES = {Astérisque},
VOLUME = {369},
year = {2015},
pages = {325--374},
issn = {0303-1179},
isbn = {978-2-85629-805-3},
mrclass = {14L05 (14G22)},
mrnumber = {3379639},
mrreviewer = {Eva Viehmann},
zblnumber = {1326.14109},
} -
[farguesfontaine] L. Fargues and J. Fontaine, "Vector bundles on curves and $p$-adic Hodge theory," in Automorphic Forms and Galois Representations. Vol. 2, Cambridge Univ. Press, Cambridge, 2014, vol. 415, pp. 17-104.
@INCOLLECTION{farguesfontaine,
author = {Fargues, Laurent and Fontaine, Jean-Marc},
title = {Vector bundles on curves and {$p$}-adic {H}odge theory},
booktitle = {Automorphic {F}orms and {G}alois {R}epresentations. {V}ol. 2},
series = {London Math. Soc. Lecture Note Ser.},
volume = {415},
pages = {17--104},
publisher = {Cambridge Univ. Press, Cambridge},
year = {2014},
mrclass = {11F80 (11S20)},
mrnumber = {3444231},
mrreviewer = {Hui June Zhu},
zblnumber = {1353.14033},
} -
[Franke]
J. Franke, "Harmonic analysis in weighted $L_2$-spaces," Ann. Sci. École Norm. Sup. (4), vol. 31, iss. 2, pp. 181-279, 1998.
@ARTICLE{Franke,
author = {Franke, Jens},
title = {Harmonic analysis in weighted {$L_2$}-spaces},
journal = {Ann. Sci. École Norm. Sup. (4)},
fjournal = {Annales Scientifiques de l'École Normale Supérieure. Quatrième Série},
volume = {31},
year = {1998},
number = {2},
pages = {181--279},
issn = {0012-9593},
mrclass = {11F75 (11F70 22E41)},
mrnumber = {1603257},
doi = {10.1016/S0012-9593(98)80015-3},
url = {http://dx.doi.org/10.1016/S0012-9593(98)80015-3},
zblnumber = {0938.11026},
} -
[shin-appendix]
W. Goldring, "Galois representations associated to holomorphic limits of discrete series," Compos. Math., vol. 150, iss. 2, pp. 191-228, 2014.
@ARTICLE{shin-appendix,
author = {Goldring, Wushi},
title = {Galois representations associated to holomorphic limits of discrete series},
journal = {Compos. Math.},
fjournal = {Compositio Mathematica},
volume = {150},
year = {2014},
number = {2},
pages = {191--228},
issn = {0010-437X},
mrclass = {11F33 (11F55 11F70)},
mrnumber = {3177267},
mrreviewer = {Luis Alberto LomelÂ-},
doi = {10.1112/S0010437X13007355},
url = {http://dx.doi.org/10.1112/S0010437X13007355},
zblnumber = {1309.11038},
} -
[hamacher]
P. Hamacher, "The geometry of Newton strata in the reduction modulo $p$ of Shimura varieties of PEL type," Duke Math. J., vol. 164, iss. 15, pp. 2809-2895, 2015.
@ARTICLE{hamacher,
author = {Hamacher, Paul},
title = {The geometry of {N}ewton strata in the reduction modulo {$p$} of {S}himura varieties of {PEL} type},
journal = {Duke Math. J.},
fjournal = {Duke Mathematical Journal},
volume = {164},
year = {2015},
number = {15},
pages = {2809--2895},
issn = {0012-7094},
mrclass = {14G35 (14L05 20G25)},
mrnumber = {3430453},
mrreviewer = {Eva Viehmann},
doi = {10.1215/00127094-3328137},
url = {http://dx.doi.org/10.1215/00127094-3328137},
zblnumber = {1335.14008},
} -
[harris-taylor] M. Harris and R. Taylor, The Geometry and Cohomology of some Simple Shimura Varieties, Princeton University Press, Princeton, NJ, 2001, vol. 151.
@BOOK{harris-taylor,
author = {Harris, Michael and Taylor, Richard},
title = {The {G}eometry and {C}ohomology of some {S}imple {S}himura {V}arieties},
series = {Annals of Mathematics Studies},
volume = {151},
note = {With an appendix by Vladimir G. Berkovich},
publisher = {Princeton University Press, Princeton, NJ},
year = {2001},
pages = {viii+276},
isbn = {0-691-09090-4},
mrclass = {11G18 (11F70 11S37 14G35 22E45)},
mrnumber = {1876802},
mrreviewer = {James Milne},
zblnumber = {1036.11027},
} -
[huber]
R. Huber, Étale cohomology of rigid analytic varieties and adic spaces, Friedr. Vieweg & Sohn, Braunschweig, 1996.
@BOOK{huber,
author = {Huber, Roland},
title = {Étale cohomology of rigid analytic varieties and adic spaces},
series = {Aspects of Mathematics, E30},
publisher = {Friedr. Vieweg \& Sohn, Braunschweig},
year = {1996},
pages = {x+450},
isbn = {3-528-06794-2},
mrclass = {14G22 (14F20)},
mrnumber = {1734903},
mrreviewer = {Lorenzo Ramero},
doi = {10.1007/978-3-663-09991-8},
url = {http://dx.doi.org/10.1007/978-3-663-09991-8},
zblnumber = {0868.14010},
} -
[illusie-autour] L. Illusie, "Autour du théorème de monodromie locale," in Périodes $p$-adiques, Math. Soc. France, Paris, 1994, vol. 223, pp. 9-57.
@incollection{illusie-autour,
author = {Illusie, Luc},
title = {Autour du théorème de monodromie locale},
BOOKTITLE = {Périodes $p$-adiques},
VENUE={Bures-sur-Yvette, 1988},
SERIES = {Astérisque},
VOLUME = {223},
PUBLISHER={Math. Soc. France, Paris},
year = {1994},
pages = {9--57},
issn = {0303-1179},
mrclass = {14F20 (11G25 14D07 14G20)},
mrnumber = {1293970},
mrreviewer = {Adolfo QuirÂ${}^3$s},
zblnumber = {0837.14013},
} -
[jacquet-shalika]
H. Jacquet and J. A. Shalika, "On Euler products and the classification of automorphic forms. II," Amer. J. Math., vol. 103, iss. 4, pp. 777-815, 1981.
@ARTICLE{jacquet-shalika,
author = {Jacquet, H. and Shalika, J. A.},
title = {On {E}uler products and the classification of automorphic forms. {II}},
journal = {Amer. J. Math.},
fjournal = {American Journal of Mathematics},
volume = {103},
year = {1981},
number = {4},
pages = {777--815},
issn = {0002-9327},
mrclass = {10D40 (12A67 22E55)},
mrnumber = {0623137},
mrreviewer = {Freydoon Shahidi},
doi = {10.2307/2374050},
url = {http://dx.doi.org/10.2307/2374050},
zblnumber = {0491.10020},
} -
[katz] N. M. Katz, "Slope filtration of $F$-crystals," in Journées de Géométrie Algébrique de Rennes, Vol. I, Soc. Math. France, Paris, 1979, vol. 63, pp. 113-163.
@INCOLLECTION{katz,
author = {Katz, Nicholas M.},
title = {Slope filtration of {$F$}-crystals},
booktitle = {Journées de {G}éométrie {A}lgébrique de {R}ennes, {V}ol. {I}},
VENUE={{R}ennes, 1978},
series = {Astérisque},
volume = {63},
pages = {113--163},
publisher = {Soc. Math. France, Paris},
year = {1979},
mrclass = {14F30 (14G20 14L05)},
mrnumber = {0563463},
mrreviewer = {Noriko Yui},
zblnumber = {0426.14007},
} -
[kisin]
M. Kisin, "Mod $p$ points on Shimura varieties of abelian type," J. Amer. Math. Soc., vol. 30, iss. 3, pp. 819-914, 2017.
@ARTICLE{kisin,
author = {Kisin, Mark},
title = {Mod {$p$} points on {S}himura varieties of abelian type},
journal = {J. Amer. Math. Soc.},
fjournal = {Journal of the American Mathematical Society},
volume = {30},
year = {2017},
number = {3},
pages = {819--914},
issn = {0894-0347},
mrclass = {11G18 (11G10 14G35)},
mrnumber = {3630089},
doi = {10.1090/jams/867},
url = {http://dx.doi.org/10.1090/jams/867},
zblnumber = {06699460},
} -
[kisinintegral]
M. Kisin, "Integral models for Shimura varieties of abelian type," J. Amer. Math. Soc., vol. 23, iss. 4, pp. 967-1012, 2010.
@ARTICLE{kisinintegral,
author = {Kisin, Mark},
title = {Integral models for {S}himura varieties of abelian type},
journal = {J. Amer. Math. Soc.},
fjournal = {Journal of the American Mathematical Society},
volume = {23},
year = {2010},
number = {4},
pages = {967--1012},
issn = {0894-0347},
mrclass = {11G18 (14G35)},
mrnumber = {2669706},
mrreviewer = {Jeffrey D. Achter},
doi = {10.1090/S0894-0347-10-00667-3},
url = {http://dx.doi.org/10.1090/S0894-0347-10-00667-3},
zblnumber = {1280.11033},
} -
[kedlayaliu] K. S. Kedlaya and R. Liu, Relative $p$-adic Hodge Theory: Foundations, , 2015, vol. 371.
@book{kedlayaliu,
author = {Kedlaya, Kiran S. and Liu, Ruochuan},
title = {Relative {$p$}-adic {H}odge Theory: Foundations},
SERIES = {Astérisque},
VOLUME= {371},
year = {2015},
note = {239 pp.},
issn = {0303-1179},
isbn = {978-2-85629-807-7},
mrclass = {14C30 (14G22)},
mrnumber = {3379653},
mrreviewer = {Giovanni Rosso},
zblnumber = {06456685},
} -
[kottwitz-cuspidal]
R. E. Kottwitz, "Stable trace formula: cuspidal tempered terms," Duke Math. J., vol. 51, iss. 3, pp. 611-650, 1984.
@ARTICLE{kottwitz-cuspidal,
author = {Kottwitz, Robert E.},
title = {Stable trace formula: cuspidal tempered terms},
journal = {Duke Math. J.},
fjournal = {Duke Mathematical Journal},
volume = {51},
year = {1984},
number = {3},
pages = {611--650},
issn = {0012-7094},
mrclass = {11R39 (11F70 11F72 22E55)},
mrnumber = {0757954},
mrreviewer = {Jean-Pierre Labesse},
doi = {10.1215/S0012-7094-84-05129-9},
url = {http://dx.doi.org/10.1215/S0012-7094-84-05129-9},
zblnumber = {0576.22020},
} -
[kottwitz]
R. E. Kottwitz, "Isocrystals with additional structure," Compositio Math., vol. 56, iss. 2, pp. 201-220, 1985.
@ARTICLE{kottwitz,
author = {Kottwitz, Robert E.},
title = {Isocrystals with additional structure},
journal = {Compositio Math.},
fjournal = {Compositio Mathematica},
volume = {56},
year = {1985},
number = {2},
pages = {201--220},
issn = {0010-437X},
mrclass = {14L25 (14F30 14L15 20G25)},
mrnumber = {0809866},
mrreviewer = {K. F. Lai},
url = {http://www.numdam.org/item?id=CM_1985__56_2_201_0},
zblnumber = {0597.20038},
} -
[kottwitz-lambda-adic] R. E. Kottwitz, "Shimura varieties and $\lambda$-adic representations," in Automorphic forms, Shimura varieties, and $L$-functions, Vol. I (Ann Arbor, MI, 1988), Academic Press, Boston, MA, 1990, vol. 10, pp. 161-209.
@INCOLLECTION{kottwitz-lambda-adic,
author = {Kottwitz, Robert E.},
title = {Shimura varieties and {$\lambda$}-adic representations},
booktitle = {Automorphic forms, {S}himura varieties, and {$L$}-functions, {V}ol. {I} ({A}nn {A}rbor, {MI},
1988)},
series = {Perspect. Math.},
volume = {10},
pages = {161--209},
publisher = {Academic Press, Boston, MA},
year = {1990},
mrclass = {11G18 (11F70 11R39)},
mrnumber = {1044820},
zblnumber = {0743.14019},
} -
[Kottwitz-lambda]
R. E. Kottwitz, "On the $\lambda$-adic representations associated to some simple Shimura varieties," Invent. Math., vol. 108, iss. 3, pp. 653-665, 1992.
@ARTICLE{Kottwitz-lambda,
author = {Kottwitz, Robert E.},
title = {On the {$\lambda$}-adic representations associated to some simple {S}himura varieties},
journal = {Invent. Math.},
fjournal = {Inventiones Mathematicae},
volume = {108},
year = {1992},
number = {3},
pages = {653--665},
issn = {0020-9910},
mrclass = {11G18 (11F70 11F85 14G35 22E55)},
mrnumber = {1163241},
mrreviewer = {Min Ho Lee},
doi = {10.1007/BF02100620},
url = {http://dx.doi.org/10.1007/BF02100620},
zblnumber = {0765.22011},
} -
[kottwitzpoints]
R. E. Kottwitz, "Points on some Shimura varieties over finite fields," J. Amer. Math. Soc., vol. 5, iss. 2, pp. 373-444, 1992.
@ARTICLE{kottwitzpoints,
author = {Kottwitz, Robert E.},
title = {Points on some {S}himura varieties over finite fields},
journal = {J. Amer. Math. Soc.},
fjournal = {Journal of the American Mathematical Society},
volume = {5},
year = {1992},
number = {2},
pages = {373--444},
issn = {0894-0347},
mrclass = {11G18 (11G25 14G10 14G35)},
mrnumber = {1124982},
mrreviewer = {Min Ho Lee},
doi = {10.2307/2152772},
url = {http://dx.doi.org/10.2307/2152772},
zblnumber = {0796.14014},
} -
[kudla] S. S. Kudla, "The local Langlands correspondence: the non-Archimedean case," in Motives (Seattle, WA, 1991), Amer. Math. Soc., Providence, RI, 1994, vol. 55, pp. 365-391.
@INCOLLECTION{kudla,
author = {Kudla, Stephen S.},
title = {The local {L}anglands correspondence: the non-{A}rchimedean case},
booktitle = {Motives ({S}eattle, {WA},
1991)},
series = {Proc. Sympos. Pure Math.},
volume = {55},
pages = {365--391},
publisher = {Amer. Math. Soc., Providence, RI},
year = {1994},
mrclass = {11F70 (11R39 11S37 22E50)},
mrnumber = {1265559},
mrreviewer = {Stephen Gelbart},
zblnumber = {0811.11072},
} -
[labesse-lefschetz]
J. -P. Labesse, "Pseudo-coefficients très cuspidaux et $K$-théorie," Math. Ann., vol. 291, iss. 4, pp. 607-616, 1991.
@ARTICLE{labesse-lefschetz,
author = {Labesse, J.-P.},
title = {Pseudo-coefficients très cuspidaux et {$K$}-théorie},
journal = {Math. Ann.},
fjournal = {Mathematische Annalen},
volume = {291},
year = {1991},
number = {4},
pages = {607--616},
issn = {0025-5831},
mrclass = {22E46 (19K99 22E41)},
mrnumber = {1135534},
mrreviewer = {Jeffrey Fox},
doi = {10.1007/BF01445230},
url = {http://dx.doi.org/10.1007/BF01445230},
zblnumber = {0789.22028},
} -
[langlands]
R. P. Langlands, "Stable conjugacy: definitions and lemmas," Canad. J. Math., vol. 31, iss. 4, pp. 700-725, 1979.
@ARTICLE{langlands,
author = {Langlands, R. P.},
title = {Stable conjugacy: definitions and lemmas},
journal = {Canad. J. Math.},
fjournal = {Canadian Journal of Mathematics. Journal Canadien de Mathématiques},
volume = {31},
year = {1979},
number = {4},
pages = {700--725},
issn = {0008-414X},
mrclass = {10D40 (12A67 22E50)},
mrnumber = {0540901},
mrreviewer = {Joe Repka},
doi = {10.4153/CJM-1979-069-2},
url = {http://dx.doi.org/10.4153/CJM-1979-069-2},
zblnumber = {0421.12013},
} -
[lan]
K. Lan, "Elevators for degenerations of PEL structures," Math. Res. Lett., vol. 18, iss. 5, pp. 889-907, 2011.
@ARTICLE{lan,
author = {Lan, Kai-Wen},
title = {Elevators for degenerations of {PEL} structures},
journal = {Math. Res. Lett.},
fjournal = {Mathematical Research Letters},
volume = {18},
year = {2011},
number = {5},
pages = {889--907},
issn = {1073-2780},
mrclass = {11G18 (14G35)},
mrnumber = {2875862},
mrreviewer = {Eva Viehmann},
doi = {10.4310/MRL.2011.v18.n5.a7},
url = {http://dx.doi.org/10.4310/MRL.2011.v18.n5.a7},
zblnumber = {1260.14026},
} -
[lau]
E. Lau, "Smoothness of the truncated display functor," J. Amer. Math. Soc., vol. 26, iss. 1, pp. 129-165, 2013.
@ARTICLE{lau,
author = {Lau, Eike},
title = {Smoothness of the truncated display functor},
journal = {J. Amer. Math. Soc.},
fjournal = {Journal of the American Mathematical Society},
volume = {26},
year = {2013},
number = {1},
pages = {129--165},
issn = {0894-0347},
mrclass = {14F30 (14L05)},
mrnumber = {2983008},
mrreviewer = {Eva Viehmann},
doi = {10.1090/S0894-0347-2012-00744-9},
url = {http://dx.doi.org/10.1090/S0894-0347-2012-00744-9},
zblnumber = {1273.14040},
} -
[langlands-shelstad]
R. P. Langlands and D. Shelstad, "On the definition of transfer factors," Math. Ann., vol. 278, iss. 1-4, pp. 219-271, 1987.
@ARTICLE{langlands-shelstad,
author = {Langlands, R. P. and Shelstad, D.},
title = {On the definition of transfer factors},
journal = {Math. Ann.},
fjournal = {Mathematische Annalen},
volume = {278},
year = {1987},
number = {1-4},
pages = {219--271},
issn = {0025-5831},
mrclass = {11S37 (11F70 11F72 22E35 22E45 22E50)},
mrnumber = {0909227},
mrreviewer = {Ernst-Wilhelm Zink},
doi = {10.1007/BF01458070},
url = {http://dx.doi.org/10.1007/BF01458070},
zblnumber = {0644.22005},
} -
[lan-suh]
K. Lan and J. Suh, "Vanishing theorems for torsion automorphic sheaves on compact PEL-type Shimura varieties," Duke Math. J., vol. 161, iss. 6, pp. 1113-1170, 2012.
@ARTICLE{lan-suh,
author = {Lan, Kai-Wen and Suh, Junecue},
title = {Vanishing theorems for torsion automorphic sheaves on compact {PEL}-type {S}himura varieties},
journal = {Duke Math. J.},
fjournal = {Duke Mathematical Journal},
volume = {161},
year = {2012},
number = {6},
pages = {1113--1170},
issn = {0012-7094},
mrclass = {11G18 (11F75 14F17 14F30 14G35)},
mrnumber = {2913102},
mrreviewer = {Yifeng Liu},
doi = {10.1215/00127094-1548452},
url = {http://dx.doi.org/10.1215/00127094-1548452},
zblnumber = {1296.11072},
} -
[mantovan]
E. Mantovan, "On the cohomology of certain PEL-type Shimura varieties," Duke Math. J., vol. 129, iss. 3, pp. 573-610, 2005.
@ARTICLE{mantovan,
author = {Mantovan, Elena},
title = {On the cohomology of certain {PEL}-type {S}himura varieties},
journal = {Duke Math. J.},
fjournal = {Duke Mathematical Journal},
volume = {129},
year = {2005},
number = {3},
pages = {573--610},
issn = {0012-7094},
mrclass = {11G18 (11F70 14G35 14L05)},
mrnumber = {2169874},
mrreviewer = {Ulrich GÂ\P rtz},
doi = {10.1215/S0012-7094-05-12935-0},
url = {http://dx.doi.org/10.1215/S0012-7094-05-12935-0},
zblnumber = {1112.11033},
} -
[Matsushima]
Y. Matsushima, "A formula for the Betti numbers of compact locally symmetric Riemannian manifolds," J. Differential Geometry, vol. 1, pp. 99-109, 1967.
@ARTICLE{Matsushima,
author = {Matsushima, Yozô},
title = {A formula for the {B}etti numbers of compact locally symmetric {R}iemannian manifolds},
journal = {J. Differential Geometry},
fjournal = {Journal of Differential Geometry},
volume = {1},
year = {1967},
pages = {99--109},
issn = {0022-040X},
mrclass = {57.31},
mrnumber = {0222908},
mrreviewer = {S. Murakami},
doi = {10.4310/jdg/1214427883},
zblnumber = {0164.22101},
} -
[messing]
W. Messing, The crystals associated to Barsotti-Tate groups: with applications to abelian schemes, Springer-Verlag, New York, 1972, vol. 264.
@BOOK{messing,
author = {Messing, William},
title = {The crystals associated to {B}arsotti-{T}ate groups: with applications to abelian schemes},
series = {Lecture Notes in Math.},
VOLUME={264},
publisher = {Springer-Verlag, New York},
year = {1972},
pages = {iii+190},
mrclass = {14L05 (14B20 14D15 14F30 14K10)},
mrnumber = {0347836},
mrreviewer = {F. Oort},
zblnumber = {0243.14013},
doi = {10.1007/BFb0058301},
} -
[milne] J. S. Milne, "Canonical models of (mixed) Shimura varieties and automorphic vector bundles," in Automorphic Forms, Shimura Varieties, and $L$-functions, Vol. I (Ann Arbor, MI, 1988), Academic Press, Boston, MA, 1990, vol. 10, pp. 283-414.
@INCOLLECTION{milne,
author = {Milne, J. S.},
title = {Canonical models of (mixed) {S}himura varieties and automorphic vector bundles},
booktitle = {Automorphic {F}orms, {S}himura {V}arieties, and {$L$}-functions, {V}ol. {I} ({A}nn {A}rbor, {MI},
1988)},
series = {Perspect. Math.},
volume = {10},
pages = {283--414},
publisher = {Academic Press, Boston, MA},
year = {1990},
mrclass = {11G18 (11F03 11F12 14K22)},
mrnumber = {1044823},
mrreviewer = {Min Ho Lee},
zblnumber = {0704.14016},
} -
[moeglin-waldspurger]
C. Moeglin and J. -L. Waldspurger, "Le spectre résiduel de ${ GL}(n)$," Ann. Sci. École Norm. Sup. (4), vol. 22, iss. 4, pp. 605-674, 1989.
@ARTICLE{moeglin-waldspurger,
author = {M{\oe}glin, C. and Waldspurger, J.-L.},
title = {Le spectre résiduel de {${\rm GL}(n)$}},
journal = {Ann. Sci. École Norm. Sup. (4)},
fjournal = {Annales Scientifiques de l'École Normale Supérieure. Quatrième Série},
volume = {22},
year = {1989},
number = {4},
pages = {605--674},
issn = {0012-9593},
mrclass = {22E55 (11F70 22E50)},
mrnumber = {1026752},
mrreviewer = {Stephen Gelbart},
doi = {10.24033/asens.1595},
zblnumber = {0696.10023},
} -
[ngo]
B. C. Ngô, "Le lemme fondamental pour les algèbres de Lie," Publ. Math. Inst. Hautes Études Sci., iss. 111, pp. 1-169, 2010.
@ARTICLE{ngo,
author = {Ng{ô},
Bao Ch{\^{a}}u},
title = {Le lemme fondamental pour les algèbres de {L}ie},
journal = {Publ. Math. Inst. Hautes Études Sci.},
fjournal = {Publications Mathématiques. Institut de Hautes Études Scientifiques},
number = {111},
year = {2010},
pages = {1--169},
issn = {0073-8301},
mrclass = {22E35 (11S37 14D23 14G35 22E50)},
mrnumber = {2653248},
mrreviewer = {R. P. Langlands},
doi = {10.1007/s10240-010-0026-7},
url = {http://dx.doi.org/10.1007/s10240-010-0026-7},
zblnumber = {1200.22011},
} -
[oort-zink] F. Oort and T. Zink, "Families of $p$-divisible groups with constant Newton polygon," Doc. Math., vol. 7, pp. 183-201, 2002.
@ARTICLE{oort-zink,
author = {Oort, Frans and Zink, Thomas},
title = {Families of {$p$}-divisible groups with constant {N}ewton polygon},
journal = {Doc. Math.},
fjournal = {Documenta Mathematica},
volume = {7},
year = {2002},
pages = {183--201},
issn = {1431-0635},
mrclass = {14L05 (14F30)},
mrnumber = {1938119},
mrreviewer = {Oliver BÂ${}^1\!/\!_4$ltel},
zblnumber = {1022.14013},
} -
[rapoport-richartz]
M. Rapoport and M. Richartz, "On the classification and specialization of $F$-isocrystals with additional structure," Compositio Math., vol. 103, iss. 2, pp. 153-181, 1996.
@ARTICLE{rapoport-richartz,
author = {Rapoport, Michael and Richartz, M.},
title = {On the classification and specialization of {$F$}-isocrystals with additional structure},
journal = {Compositio Math.},
fjournal = {Compositio Mathematica},
volume = {103},
year = {1996},
number = {2},
pages = {153--181},
issn = {0010-437X},
mrclass = {14F30 (22E50)},
mrnumber = {1411570},
mrreviewer = {Abdellah Mokrane},
url = {http://www.numdam.org/item?id=CM_1996__103_2_153_0},
zblnumber = {0874.14008},
} -
[rapoport-zink]
M. Rapoport and T. Zink, Period Spaces for $p$-divisible Groups, Princeton University Press, Princeton, NJ, 1996, vol. 141.
@BOOK{rapoport-zink,
author = {Rapoport, M. and Zink, Th.},
title = {Period {S}paces for {$p$}-divisible {G}roups},
series = {Annals of Mathematics Studies},
volume = {141},
publisher = {Princeton University Press, Princeton, NJ},
year = {1996},
pages = {xxii+324},
isbn = {0-691-02782-X; 0-691-02781-1},
mrclass = {14G20 (11G18 14F30 14L05 14M15 20G05 20G25)},
mrnumber = {1393439},
mrreviewer = {Robert E. Kottwitz},
doi = {10.1515/9781400882601},
url = {http://dx.doi.org/10.1515/9781400882601},
zblnumber = {0873.14039},
} -
[scholzeperfectoid]
P. Scholze, "Perfectoid spaces," Publ. Math. Inst. Hautes Études Sci., vol. 116, pp. 245-313, 2012.
@ARTICLE{scholzeperfectoid,
author = {Scholze, Peter},
title = {Perfectoid spaces},
journal = {Publ. Math. Inst. Hautes Études Sci.},
fjournal = {Publications Mathématiques. Institut de Hautes Études Scientifiques},
volume = {116},
year = {2012},
pages = {245--313},
issn = {0073-8301},
mrclass = {14G99},
mrnumber = {3090258},
mrreviewer = {Jean-Marc Fontaine},
doi = {10.1007/s10240-012-0042-x},
url = {http://dx.doi.org/10.1007/s10240-012-0042-x},
zblnumber = {1263.14022},
} -
[scholzeLKgen]
P. Scholze, "The Langlands-Kottwitz method and deformation spaces of $p$-divisible groups," J. Amer. Math. Soc., vol. 26, iss. 1, pp. 227-259, 2013.
@ARTICLE{scholzeLKgen,
author = {Scholze, Peter},
title = {The {L}anglands-{K}ottwitz method and deformation spaces of {$p$}-divisible groups},
journal = {J. Amer. Math. Soc.},
fjournal = {Journal of the American Mathematical Society},
volume = {26},
year = {2013},
number = {1},
pages = {227--259},
issn = {0894-0347},
mrclass = {11G18 (14G22 14G35 14L05)},
mrnumber = {2983011},
mrreviewer = {Mihran Papikian},
doi = {10.1090/S0894-0347-2012-00753-X},
url = {http://dx.doi.org/10.1090/S0894-0347-2012-00753-X},
zblnumber = {06168122},
} -
[scholzeLLC]
P. Scholze, "The local Langlands correspondence for $\mathrm{GL}_n$ over $p$-adic fields," Invent. Math., vol. 192, iss. 3, pp. 663-715, 2013.
@ARTICLE{scholzeLLC,
author = {Scholze, Peter},
title = {The local {L}anglands correspondence for {$\mathrm{GL}_n$} over {$p$}-adic fields},
journal = {Invent. Math.},
fjournal = {Inventiones Mathematicae},
volume = {192},
year = {2013},
number = {3},
pages = {663--715},
issn = {0020-9910},
mrclass = {22E50 (11G18 14G35)},
mrnumber = {3049932},
mrreviewer = {Maarten Sander Solleveld},
doi = {10.1007/s00222-012-0420-5},
url = {http://dx.doi.org/10.1007/s00222-012-0420-5},
zblnumber = {1305.22025},
} -
[scholze-lubintate]
P. Scholze, "On torsion in the cohomology of locally symmetric varieties," Ann. of Math. (2), vol. 182, iss. 3, pp. 945-1066, 2015.
@ARTICLE{scholze-lubintate,
author = {Scholze, Peter},
title = {On torsion in the cohomology of locally symmetric varieties},
journal = {Ann. of Math. (2)},
fjournal = {Annals of Mathematics. Second Series},
volume = {182},
year = {2015},
number = {3},
pages = {945--1066},
issn = {0003-486X},
mrclass = {11S37},
mrnumber = {3418533},
mrreviewer = {Kimball L. Martin},
doi = {10.4007/annals.2015.182.3.3},
url = {http://dx.doi.org/10.4007/annals.2015.182.3.3},
zblnumber = {1345.14031},
} -
[scholze]
P. Scholze, "On torsion in the cohomology of locally symmetric varieties," Ann. of Math. (2), vol. 182, iss. 3, pp. 945-1066, 2015.
@ARTICLE{scholze,
author = {Scholze, Peter},
title = {On torsion in the cohomology of locally symmetric varieties},
journal = {Ann. of Math. (2)},
fjournal = {Annals of Mathematics. Second Series},
volume = {182},
year = {2015},
number = {3},
pages = {945--1066},
issn = {0003-486X},
mrclass = {11S37},
mrnumber = {3418533},
mrreviewer = {Kimball L. Martin},
doi = {10.4007/annals.2015.182.3.3},
url = {http://dx.doi.org/10.4007/annals.2015.182.3.3},
zblnumber = {1345.14031},
} -
[SGA7.2]
Groupes de monodromie en géométrie algébrique, Deligne, P. and Katz, N., Eds., Springer-Verlag, New York, 1973, vol. 340.
@BOOK{SGA7.2, title = {Groupes de monodromie en géométrie algébrique},
series = {Lecture Notes in Math.},
VOLUME={340},
note = {Séminaire de Géométrie Algébrique du Bois-Marie 1967--1969 (SGA 7 II)},
EDITOR={Deligne, Pierre and Katz, N},
publisher = {Springer-Verlag, New York},
year = {1973},
pages = {x+438},
mrclass = {14-06},
mrnumber = {0354657},
zblnumber = {0258.00005},
doi = {10.1007/BFb0060505},
} -
[shin-galois]
S. W. Shin, "Galois representations arising from some compact Shimura varieties," Ann. of Math. (2), vol. 173, iss. 3, pp. 1645-1741, 2011.
@ARTICLE{shin-galois,
author = {Shin, Sug Woo},
title = {Galois representations arising from some compact {S}himura varieties},
journal = {Ann. of Math. (2)},
fjournal = {Annals of Mathematics. Second Series},
volume = {173},
year = {2011},
number = {3},
pages = {1645--1741},
issn = {0003-486X},
mrclass = {11F80 (11G18)},
mrnumber = {2800722},
mrreviewer = {Peter Scholze},
doi = {10.4007/annals.2011.173.3.9},
url = {http://dx.doi.org/10.4007/annals.2011.173.3.9},
zblnumber = {1269.11053},
} -
[shin-torsion]
S. W. Shin, "Supercuspidal part of the ${ mod}\,l$ cohomology of ${ GU}(1,n-1)$-Shimura varieties," J. Reine Angew. Math., vol. 705, pp. 1-21, 2015.
@ARTICLE{shin-torsion,
author = {Shin, Sug Woo},
title = {Supercuspidal part of the {${\rm mod}\,l$} cohomology of {${\rm GU}(1,n-1)$}-{S}himura varieties},
journal = {J. Reine Angew. Math.},
fjournal = {Journal für die Reine und Angewandte Mathematik. [Crelle's Journal]},
volume = {705},
year = {2015},
pages = {1--21},
issn = {0075-4102},
mrclass = {11G18 (22E50)},
mrnumber = {3377388},
mrreviewer = {Dipendra Prasad},
doi = {10.1515/crelle-2013-0057},
url = {http://dx.doi.org/10.1515/crelle-2013-0057},
zblnumber = {1330.11042},
} -
[scholze-shin]
P. Scholze and S. W. Shin, "On the cohomology of compact unitary group Shimura varieties at ramified split places," J. Amer. Math. Soc., vol. 26, iss. 1, pp. 261-294, 2013.
@ARTICLE{scholze-shin,
author = {Scholze, Peter and Shin, Sug Woo},
title = {On the cohomology of compact unitary group {S}himura varieties at ramified split places},
journal = {J. Amer. Math. Soc.},
fjournal = {Journal of the American Mathematical Society},
volume = {26},
year = {2013},
number = {1},
pages = {261--294},
issn = {0894-0347},
mrclass = {11G18 (11F70 11F80 11S37 14G35 22E50)},
mrnumber = {2983012},
mrreviewer = {Wei Zhang},
doi = {10.1090/S0894-0347-2012-00752-8},
url = {http://dx.doi.org/10.1090/S0894-0347-2012-00752-8},
zblnumber = {06168123},
} -
[scholzeweinstein]
P. Scholze and J. Weinstein, "Moduli of $p$-divisible groups," Camb. J. Math., vol. 1, iss. 2, pp. 145-237, 2013.
@ARTICLE{scholzeweinstein,
author = {Scholze, Peter and Weinstein, Jared},
title = {Moduli of {$p$}-divisible groups},
journal = {Camb. J. Math.},
fjournal = {Cambridge Journal of Mathematics},
volume = {1},
year = {2013},
number = {2},
pages = {145--237},
issn = {2168-0930},
mrclass = {14L05 (11G25 14C30 14D20)},
mrnumber = {3272049},
mrreviewer = {Rui Miguel Saramago},
doi = {10.4310/CJM.2013.v1.n2.a1},
url = {http://dx.doi.org/10.4310/CJM.2013.v1.n2.a1},
zblnumber = {1349.14149},
} -
@ARTICLE{thorne,
author = {Thorne, Jack A.},
title = {Raising the level for {${\rm GL}_{n}$}},
journal = {Forum Math. Sigma},
fjournal = {Forum of Mathematics. Sigma},
volume = {2},
year = {2014},
pages = {e16, 35},
issn = {2050-5094},
mrclass = {11F33 (11R39 22E50)},
mrnumber = {3264255},
mrreviewer = {Gabor Wiese},
doi = {10.1017/fms.2014.14},
url = {http://dx.doi.org/10.1017/fms.2014.14},
zblnumber = {1296.11034},
} -
[waldspurger]
J. -L. Waldspurger, "Le lemme fondamental implique le transfert," Compositio Math., vol. 105, iss. 2, pp. 153-236, 1997.
@ARTICLE{waldspurger,
author = {Waldspurger, J.-L.},
title = {Le lemme fondamental implique le transfert},
journal = {Compositio Math.},
fjournal = {Compositio Mathematica},
volume = {105},
year = {1997},
number = {2},
pages = {153--236},
issn = {0010-437X},
mrclass = {22E50 (11F72 11F85 22E35)},
mrnumber = {1440722},
mrreviewer = {David Manderscheid},
doi = {10.1023/A:1000103112268},
url = {http://dx.doi.org/10.1023/A:1000103112268},
zblnumber = {0871.22005},
} -
[wedhorn]
T. Wedhorn, "Ordinariness in good reductions of Shimura varieties of PEL-type," Ann. Sci. École Norm. Sup. (4), vol. 32, iss. 5, pp. 575-618, 1999.
@ARTICLE{wedhorn,
author = {Wedhorn, Torsten},
title = {Ordinariness in good reductions of {S}himura varieties of {PEL}-type},
journal = {Ann. Sci. École Norm. Sup. (4)},
fjournal = {Annales Scientifiques de l'École Normale Supérieure. Quatrième Série},
volume = {32},
year = {1999},
number = {5},
pages = {575--618},
issn = {0012-9593},
mrclass = {11G18 (14G35 14L05)},
mrnumber = {1710754},
mrreviewer = {Ben Moonen},
doi = {10.1016/S0012-9593(01)80001-X},
zblnumber = {0983.14024},
}