Functoriality, Smith theory, and the Brauer homomorphism

Abstract

If $\sigma$ is an automorphism of order $p$ of the semisimple group $\mathbf{G}$, there is a natural correspondence between \rm mod $p$ cohomological automorphic forms on $\mathbf{G}$ and $\mathbf{G}^{\sigma}$. We describe this correspondence in the global and local settings.

  • [Ash] Go to document A. Ash, "Smith theory and Hecke operators," J. Algebra, vol. 259, iss. 1, pp. 43-58, 2003.
    @article{Ash, mrkey = {1953707},
      author = {Ash, Avner},
      title = {Smith theory and {H}ecke operators},
      journal = {J. Algebra},
      fjournal = {Journal of Algebra},
      volume = {259},
      year = {2003},
      number = {1},
      pages = {43--58},
      issn = {0021-8693},
      coden = {JALGA4},
      mrclass = {11F75 (11F60)},
      mrnumber = {1953707},
      mrreviewer = {Stefan K{ü}hnlein},
      doi = {10.1016/S0021-8693(02)00547-1},
      zblnumber = {1045.11034},
      }
  • [Ash2] Go to document A. Ash, "Direct sums of $\bmod p$ characters of ${ GAL}(\overline{\Bbb Q}/{\Bbb Q})$ and the homology of $GL(n,{\Bbb Z})$," Comm. Algebra, vol. 41, iss. 5, pp. 1751-1775, 2013.
    @article{Ash2, mrkey = {3062822},
      author = {Ash, Avner},
      title = {Direct sums of {$\bmod p$} characters of {${\rm GAL}(\overline{\Bbb Q}/{\Bbb Q})$} and the homology of {$GL(n,{\Bbb Z})$}},
      journal = {Comm. Algebra},
      fjournal = {Communications in Algebra},
      volume = {41},
      year = {2013},
      number = {5},
      pages = {1751--1775},
      issn = {0092-7872},
      mrclass = {11F75 (11F67 11F80)},
      mrnumber = {3062822},
      mrreviewer = {Lei Yang},
      doi = {10.1080/00927872.2011.649508},
      zblnumber = {06194716},
      }
  • [BV] Go to document N. Bergeron and A. Venkatesh, "The asymptotic growth of torsion homology for arithmetic groups," J. Inst. Math. Jussieu, vol. 12, iss. 2, pp. 391-447, 2013.
    @article{BV, mrkey = {3028790},
      author = {Bergeron, Nicolas and Venkatesh, Akshay},
      title = {The asymptotic growth of torsion homology for arithmetic groups},
      journal = {J. Inst. Math. Jussieu},
      fjournal = {Journal of the Institute of Mathematics of Jussieu. JIMJ. Journal de l'Institut de Mathématiques de Jussieu},
      volume = {12},
      year = {2013},
      number = {2},
      pages = {391--447},
      issn = {1474-7480},
      mrclass = {57M25 (22E47)},
      mrnumber = {3028790},
      mrreviewer = {Paul E. Gunnells},
      doi = {10.1017/S1474748012000667},
      zblnumber = {1266.22013},
      }
  • [BZ] Go to document I. N. Bernstein and A. V. Zelevinsky, "Induced representations of reductive $\mathfrak{p}$-adic groups. I," Ann. Sci. École Norm. Sup., vol. 10, iss. 4, pp. 441-472, 1977.
    @article{BZ, mrkey = {0579172},
      author = {Bernstein, I. N. and Zelevinsky, A. V.},
      title = {Induced representations of reductive {$\mathfrak{p}$}-adic groups. {I}},
      journal = {Ann. Sci. École Norm. Sup.},
      fjournal = {Annales Scientifiques de l'École Normale Supérieure. Quatrième Série},
      volume = {10},
      year = {1977},
      number = {4},
      pages = {441--472},
      issn = {0012-9593},
      mrclass = {22E50},
      mrnumber = {0579172},
      url = {http://www.numdam.org/item?id=ASENS_1977_4_10_4_441_0},
      zblnumber = {0412.22015},
      }
  • [Bernstein] J. Bernstein, Course notes of a course on $p$-adic groups.
    @misc{Bernstein,
      author={Bernstein, J.},
      title = {Course notes of a course on $p$-adic groups},
      }
  • [Borel] A. Borel, "Automorphic $L$-functions," in Automorphic Forms, Representations and $L$-Functions, Providence, R.I.: Amer. Math. Soc., 1979, vol. 33, pp. 27-61.
    @incollection{Borel, mrkey = {0546608},
      author = {Borel, A.},
      title = {Automorphic {$L$}-functions},
      booktitle = {Automorphic Forms, Representations and {$L$}-Functions},
      venue = {{P}roc. {S}ympos. {P}ure {M}ath., {O}regon {S}tate {U}niv., {C}orvallis, {O}re., 1977, {P}art 2},
      series = {Proc. Sympos. Pure Math.},
      volume = {33},
      pages = {27--61},
      publisher = {Amer. Math. Soc.},
      address = {Providence, R.I.},
      year = {1979},
      mrclass = {10D40 (12A67 22E50)},
      mrnumber = {0546608},
      mrreviewer = {Yasuhiro Asoo},
      zblnumber = {0412.10017},
      }
  • [BorelTits] Go to document A. Borel and J. Tits, "Groupes réductifs," Publ. Math. Inst. Hautes Études Sci., vol. 27, pp. 55-150, 1965.
    @article{BorelTits, mrkey = {0207712},
      author = {Borel, Armand and Tits, Jacques},
      title = {Groupes réductifs},
      journal = {Publ. Math. Inst. Hautes Études Sci.},
      fjournal = {Institut des Hautes Études Scientifiques. Publications Mathématiques},
      volume = {27},
      year = {1965},
      pages = {55--150},
      issn = {0073-8301},
      mrclass = {14.50 (20.75)},
      mrnumber = {0207712},
      mrreviewer = {F. D. Veldkamp},
      doi = {10.1007/BF02684375},
      zblnumber = {0145.17402},
      }
  • [Bourbaki] Go to document N. Bourbaki, Algebra II. Chapters 4–7, New York: Springer-Verlag, 2003.
    @book{Bourbaki, mrkey = {1994218},
      author = {Bourbaki, Nicolas},
      title = {Algebra {II}. {C}hapters 4--7},
      series = {Elements of Mathematics (Berlin)},
      note = {translated from the 1981 French edition by P. M. Cohn and J. Howie, Reprint of the 1990 English edition [Springer, Berlin; MR1080964},
      publisher = {Springer-Verlag},
      year = {2003},
      pages = {viii+461},
      isbn = {3-540-00706-7},
      mrclass = {00A05 (12-01 13-01)},
      mrnumber = {1994218},
      doi = {10.1007/978-3-642-61698-3},
      address = {New York},
      zblnumber = {1017.12001},
      }
  • [BG] K. Buzzard and T. Gee, The conjectural connections between automorphic representations and Galois representations, 2010.
    @misc{BG,
      author = {Buzzard, K. and Gee, T.},
      title = {The conjectural connections between automorphic representations and {G}alois representations},
      note = {preprint},
      arxiv = {1009.0785},
      year = {2010},
      }
  • [Cartier] P. Cartier, "Representations of $p$-adic groups: a survey," in Automorphic Forms, Representations and $L$-Functions, Providence, R.I.: Amer. Math. Soc., 1979, vol. 33, pp. 111-155.
    @incollection{Cartier, mrkey = {0546593},
      author = {Cartier, P.},
      title = {Representations of {$p$}-adic groups: a survey},
      booktitle = {Automorphic Forms, Representations and {$L$}-Functions},
      venue = {{P}roc. {S}ympos. {P}ure {M}ath., {O}regon {S}tate {U}niv., {C}orvallis, {O}re., 1977, {P}art 1},
      series = {Proc. Sympos. Pure Math.},
      volume = {33},
      pages = {111--155},
      publisher = {Amer. Math. Soc.},
      address = {Providence, R.I.},
      year = {1979},
      mrclass = {22E50},
      mrnumber = {0546593},
      mrreviewer = {Allan J. Silberger},
      zblnumber = {0421.22010},
      }
  • [Casselman] W. Casselman, Introduction to the theory of admissible representations.
    @misc{Casselman,
      author = {Casselman, W.},
      title = {Introduction to the theory of admissible representations},
      }
  • [Clozel2] L. Clozel, "Formes modulaires mod $p$, changement de base et théorie d’Iwasawa," Rend. Mat. Appl. (7), vol. 35, iss. 1-2, pp. 35-46, 2014.
    @article{Clozel2, mrey = {3241362},
      author = {Clozel, Laurent},
      title = {Formes modulaires mod $p$, changement de base et théorie d'{I}wasawa},
      JOURNAL = {Rend. Mat. Appl. (7)},
      FJOURNAL = {Rendiconti di Matematica e delle sue Applicazioni. Serie {V}{I}{I}},
      VOLUME = {35},
      YEAR = {2014},
      NUMBER = {1-2},
      PAGES = {35--46},
      ISSN = {1120-7183},
      MRCLASS = {11F11 (11R23)},
      MRNUMBER = {3241362},
      }
  • [Clozel] Go to document L. Clozel, "Formes modulaires sur la $\Bbb Z_p$-extension cyclotomique de $\Bbb Q$," Pacific J. Math., vol. 268, iss. 2, pp. 259-274, 2014.
    @article{Clozel, mrkey = {3227435},
      author = {Clozel, Laurent},
      title = {Formes modulaires sur la {$\Bbb Z\sb p$}-extension cyclotomique de {$\Bbb Q$}},
      journal = {Pacific J. Math.},
      fjournal = {Pacific Journal of Mathematics},
      volume = {268},
      year = {2014},
      number = {2},
      pages = {259--274},
      issn = {0030-8730},
      mrclass = {11F11},
      mrnumber = {3227435},
      doi = {10.2140/pjm.2014.268.259},
      zblnumber = {06335993},
      }
  • [DeligneLusztig] Go to document P. Deligne and G. Lusztig, "Representations of reductive groups over finite fields," Ann. of Math., vol. 103, iss. 1, pp. 103-161, 1976.
    @article{DeligneLusztig, mrkey = {0393266},
      author = {Deligne, P. and Lusztig, G.},
      title = {Representations of reductive groups over finite fields},
      journal = {Ann. of Math.},
      fjournal = {Annals of Mathematics. Second Series},
      volume = {103},
      year = {1976},
      number = {1},
      pages = {103--161},
      issn = {0003-486X},
      mrclass = {20G05 (14M15)},
      mrnumber = {0393266},
      mrreviewer = {S. I. Gelfand},
      doi = {10.2307/1971021},
      zblnumber = {0336.20029},
      }
  • [emerton] Go to document M. Emerton, "A local-global compatibility conjecture in the $p$-adic Langlands programme for ${ GL}_{2/{\Bbb Q}}$," Pure Appl. Math. Q., vol. 2, iss. 2, Special Issue: In honor of John H. Coates. Part 2, pp. 279-393, 2006.
    @article{emerton, mrkey = {2251474},
      author = {Emerton, Matthew},
      title = {A local-global compatibility conjecture in the {$p$}-adic {L}anglands programme for {${\rm GL}\sb {2/{\Bbb Q}}$}},
      journal = {Pure Appl. Math. Q.},
      fjournal = {Pure and Applied Mathematics Quarterly},
      volume = {2},
      year = {2006},
      number = {2, Special Issue: In honor of John H. Coates. Part 2},
      pages = {279--393},
      issn = {1558-8599},
      mrclass = {11S37 (11F70 11F80 22E55)},
      mrnumber = {2251474},
      mrreviewer = {David L. Savitt},
      doi = {10.4310/PAMQ.2006.v2.n2.a1},
      zblnumber = {1254.11106},
      }
  • [GS] Go to document W. T. Gan and G. Savin, "Real and global lifts from $ PGL_3$ to $G_2$," Int. Math. Res. Not., vol. 2003, iss. 50, pp. 2699-2724, 2003.
    @article{GS, mrkey = {2017248},
      author = {Gan, Wee Teck and Savin, Gordan},
      title = {Real and global lifts from {$\rm PGL\sb 3$} to {$G\sb 2$}},
      journal = {Int. Math. Res. Not.},
      fjournal = {International Mathematics Research Notices},
      year = {2003},
      number = {50},
      pages = {2699--2724},
      issn = {1073-7928},
      mrclass = {11F70 (20G30 22E55)},
      mrnumber = {2017248},
      mrreviewer = {B. Sury},
      doi = {10.1155/S1073792803130607},
      volume = {2003},
      zblnumber = {1037.22033},
      }
  • [Glauberman] Go to document G. Glauberman, "Correspondences of characters for relatively prime operator groups.," Canad. J. Math., vol. 20, pp. 1465-1488, 1968.
    @article{Glauberman, mrkey = {0232866},
      author = {Glauberman, George},
      title = {Correspondences of characters for relatively prime operator groups.},
      journal = {Canad. J. Math.},
      fjournal = {Canadian Journal of Mathematics. Journal Canadien de Mathématiques},
      volume = {20},
      year = {1968},
      pages = {1465--1488},
      issn = {0008-414X},
      mrclass = {20.80},
      mrnumber = {0232866},
      mrreviewer = {I. M. Isaacs},
      doi = {10.4153/CJM-1968-148-x},
      zblnumber = {0167.02602},
      }
  • [Gross] Go to document B. H. Gross, "On the Satake isomorphism," in Galois Representations in Arithmetic Algebraic Geometry, Cambridge: Cambridge Univ. Press, 1998, vol. 254, pp. 223-237.
    @incollection{Gross, mrkey = {1696481},
      author = {Gross, Benedict H.},
      title = {On the {S}atake isomorphism},
      booktitle = {Galois Representations in Arithmetic Algebraic Geometry},
      venue = {{D}urham, 1996},
      series = {London Math. Soc. Lecture Note Ser.},
      volume = {254},
      pages = {223--237},
      publisher = {Cambridge Univ. Press},
      address = {Cambridge},
      year = {1998},
      mrclass = {22E50 (11F70)},
      mrnumber = {1696481},
      mrreviewer = {David Manderscheid},
      doi = {10.1017/CBO9780511662010.006},
      zblnumber = {0996.11038},
      }
  • [Gunnells] P. Gunnells and D. Yasaki, On the growth of torsion in the cohomology of arithmetic groups.
    @misc{Gunnells,
      author = {Gunnells, P. and Yasaki, D.},
      title = {On the growth of torsion in the cohomology of arithmetic groups},
      note = {in preparation},
      }
  • [HainesRostami] Go to document T. J. Haines and S. Rostami, "The Satake isomorphism for special maximal parahoric Hecke algebras," Represent. Theory, vol. 14, pp. 264-284, 2010.
    @article{HainesRostami, mrkey = {2602034},
      author = {Haines, Thomas J. and Rostami, Sean},
      title = {The {S}atake isomorphism for special maximal parahoric {H}ecke algebras},
      journal = {Represent. Theory},
      fjournal = {Representation Theory. An Electronic Journal of the American Mathematical Society},
      volume = {14},
      year = {2010},
      pages = {264--284},
      issn = {1088-4165},
      mrclass = {20G25 (11E95 11G18 14G35 22E50)},
      mrnumber = {2602034},
      mrreviewer = {Rainer Schulze-Pillot},
      doi = {10.1090/S1088-4165-10-00370-5},
      zblnumber = {1251.22013},
      }
  • [HenniartVigneras] G. Henniart and M. Vignéras, "A Satake isomorphism for representations modulo $p$ of reductive groups over local fields," J. reine angew. Math., vol. 701, pp. 33-75, 2015.
    @article{HenniartVigneras, mrkey = {3331726},
      author = {Henniart, Guy and Vign{é}ras, Marie-France},
      title = {A {S}atake isomorphism for representations modulo {$p$} of reductive groups over local fields},
      journal = {J. reine angew. Math.},
      fjournal = {Journal für die Reine und Angewandte Mathematik. [Crelle's Journal]},
      volume = {701},
      year = {2015},
      pages = {33--75},
      issn = {0075-4102},
      mrclass = {22E50 (20G25)},
      mrnumber = {3331726},
      zblnumber = {06424795},
     }
  • [Joyner] D. Joyner, "On finite dimensional representations of non-connected reductive groups," J. Lie Theory, vol. 10, iss. 2, pp. 269-284, 2000.
    @article{Joyner, mrkey = {1774860},
      author = {Joyner, David},
      title = {On finite dimensional representations of non-connected reductive groups},
      journal = {J. Lie Theory},
      fjournal = {Journal of Lie Theory},
      volume = {10},
      year = {2000},
      number = {2},
      pages = {269--284},
      issn = {0949-5932},
      mrclass = {20G05},
      mrnumber = {1774860},
      mrreviewer = {Timo Neuvonen},
      zblnumber = {0986.20043},
      }
  • [Kionke] Go to document S. Kionke, "On lower bounds for cohomology growth in $p$-adic analytic towers," Math. Z., vol. 277, iss. 3-4, pp. 709-723, 2014.
    @article{Kionke, mrkey = {3229961},
      author = {Kionke, Steffen},
      title = {On lower bounds for cohomology growth in {$p$}-adic analytic towers},
      journal = {Math. Z.},
      fjournal = {Mathematische Zeitschrift},
      volume = {277},
      year = {2014},
      number = {3-4},
      pages = {709--723},
      issn = {0025-5874},
      mrclass = {20J06 (11F75 57M07)},
      mrnumber = {3229961},
      mrreviewer = {Stefan Witzel},
      doi = {10.1007/s00209-013-1273-3},
      zblnumber = {06323331},
      }
  • [KottwitzShelstad] R. E. Kottwitz and D. Shelstad, Foundations of Twisted Endoscopy, , 1999, vol. 255.
    @book{KottwitzShelstad, mrkey = {1687096},
      author = {Kottwitz, Robert E. and Shelstad, Diana},
      title = {Foundations of Twisted Endoscopy},
      series = {Astérisque},
      fjournal = {Astérisque},
      volume = {255},
      year = {1999},
      pages = {vi+190},
      issn = {0303-1179},
      mrclass = {22E55 (11F70 11R34 22-02 22E50)},
      mrnumber = {1687096},
      mrreviewer = {Volker J. Heiermann},
      zblnumber = {0958.22013},
      }
  • [KrainesSchochet] Go to document D. Kraines and C. Schochet, "Differentials in the Eilenberg-Moore spectral sequence," J. Pure Appl. Algebra, vol. 2, iss. 2, pp. 131-148, 1972.
    @article{KrainesSchochet, mrkey = {0300285},
      author = {Kraines, David and Schochet, Claude},
      title = {Differentials in the {E}ilenberg-{M}oore spectral sequence},
      journal = {J. Pure Appl. Algebra},
      fjournal = {Journal of Pure and Applied Algebra},
      volume = {2},
      year = {1972},
      number = {2},
      pages = {131--148},
      issn = {0022-4049},
      mrclass = {55H20},
      mrnumber = {0300285},
      mrreviewer = {J. Stasheff},
      doi = {10.1016/0022-4049(72)90018-7},
      zblnumber = {0237.55016},
      }
  • [Langlandstori] Go to document R. P. Langlands, "Representations of abelian algebraic groups," Pacific J. Math., vol. 181, iss. Special Issue, pp. 231-250, 1997.
    @article{Langlandstori, mrkey = {1610871},
      author = {Langlands, R. P.},
      title = {Representations of abelian algebraic groups},
      note = {Olga Taussky-Todd: in memoriam},
      journal = {Pacific J. Math.},
      fjournal = {Pacific Journal of Mathematics},
      volume = {181},
      year = {1997},
      number = {Special Issue},
      pages = {231--250},
      issn = {0030-8730},
      coden = {PJMAAI},
      mrclass = {11R39 (22E55)},
      mrnumber = {1610871},
      mrreviewer = {Volker J. Heiermann},
      doi = {10.2140/pjm.1997.181.231},
      }
  • [Mu] Go to document W. Müller and J. Pfaff, "On the growth of torsion in the cohomology of arithmetic groups," Math. Ann., vol. 359, iss. 1-2, pp. 537-555, 2014.
    @article{Mu, mrkey = {3201905},
      author = {M{ü}ller, Werner and Pfaff, Jonathan},
      title = {On the growth of torsion in the cohomology of arithmetic groups},
      journal = {Math. Ann.},
      fjournal = {Mathematische Annalen},
      volume = {359},
      year = {2014},
      number = {1-2},
      pages = {537--555},
      issn = {0025-5831},
      mrclass = {20G35 (14L99)},
      mrnumber = {3201905},
      mrreviewer = {B. Sury},
      doi = {10.1007/s00208-014-1014-x},
      zblnumber = {06312297},
      }
  • [PlatonovRapinchuk] V. Platonov and A. Rapinchuk, Algebraic Groups and Number Theory, Boston: Academic Press, 1994, vol. 139.
    @book{PlatonovRapinchuk, mrkey = {1278263},
      author = {Platonov, Vladimir and Rapinchuk, Andrei},
      title = {Algebraic Groups and Number Theory},
      series = {Pure Appl. Math.},
      volume = {139},
      note = {translated from the 1991 Russian original by Rachel Rowen},
      publisher = {Academic Press},
      address = {Boston},
      year = {1994},
      pages = {xii+614},
      isbn = {0-12-558180-7},
      mrclass = {11E57 (11-02 20Gxx)},
      mrnumber = {1278263},
      zblnumber = {0841.20046},
      }
  • [RSref] Go to document J. Rohlfs and B. Speh, "Lefschetz numbers and twisted stabilized orbital integrals," Math. Ann., vol. 296, iss. 2, pp. 191-214, 1993.
    @article{RSref, mrkey = {1219899},
      author = {Rohlfs, J. and Speh, B.},
      title = {Lefschetz numbers and twisted stabilized orbital integrals},
      journal = {Math. Ann.},
      fjournal = {Mathematische Annalen},
      volume = {296},
      year = {1993},
      number = {2},
      pages = {191--214},
      issn = {0025-5831},
      coden = {MAANA},
      mrclass = {11F75 (11F72 22E40)},
      mrnumber = {1219899},
      mrreviewer = {Joe Repka},
      doi = {10.1007/BF01445102},
      zblnumber = {0808.11039},
      }
  • [Satake] Go to document I. Satake, "Theory of spherical functions on reductive algebraic groups over $\mathfrak{p}$-adic fields," Publ. Math. Inst. Hautes Études Sci., vol. 18, pp. 5-69, 1963.
    @article{Satake, mrkey = {0195863},
      author = {Satake, Ichir{ô}},
      title = {Theory of spherical functions on reductive algebraic groups over {$\mathfrak{p}$}-adic fields},
      journal = {Publ. Math. Inst. Hautes Études Sci.},
      fjournal = {Institut des Hautes Études Scientifiques. Publications Mathématiques},
      volume = {18},
      year = {1963},
      pages = {5--69},
      issn = {0073-8301},
      mrclass = {22.60 (14.50)},
      mrnumber = {0195863},
      mrreviewer = {T. Ono},
      doi = {10.1007/BF02684781},
      zblnumber = {0122.28501},
      }
  • [Sengun] Go to document M. H. cSengün, "On the integral cohomology of Bianchi groups," Exp. Math., vol. 20, iss. 4, pp. 487-505, 2011.
    @article{Sengun, mrkey = {2859903},
      author = {{\c{S}}eng{ü}n, Mehmet Haluk},
      title = {On the integral cohomology of {B}ianchi groups},
      journal = {Exp. Math.},
      fjournal = {Experimental Mathematics},
      volume = {20},
      year = {2011},
      number = {4},
      pages = {487--505},
      issn = {1058-6458},
      mrclass = {22E40 (11F41 11F75 20H10 20J06)},
      mrnumber = {2859903},
      mrreviewer = {Albert Ruiz},
      doi = {10.1080/10586458.2011.594671},
      zblnumber = {1269.22007},
      }
  • [SerreQuat] Go to document . J-P. Serre, "Two letters on quaternions and modular forms (mod $p$)," Israel J. Math., vol. 95, pp. 281-299, 1996.
    @article{SerreQuat, mrkey = {1418297},
      author = {Serre, {\relax J-P}},
      title = {Two letters on quaternions and modular forms (mod {$p$})},
      note = {with introduction, appendix and references by R. Livn{é}},
      journal = {Israel J. Math.},
      fjournal = {Israel Journal of Mathematics},
      volume = {95},
      year = {1996},
      pages = {281--299},
      issn = {0021-2172},
      coden = {ISJMAP},
      mrclass = {11F33 (11R52)},
      mrnumber = {1418297},
      mrreviewer = {Fernando Q. Gouv{ê}a},
      doi = {10.1007/BF02761043},
      zblnumber = {0870.11030},
      }
  • [GaloisCohomology] . J-P. Serre, Cohomologie Galoisienne, New York: Springer-Verlag, 1973, vol. 5.
    @book{GaloisCohomology, mrkey = {0404227},
      author = {Serre, {\relax J-P}},
      title = {Cohomologie {G}aloisienne},
      series = {Lecture Notes in Math.},
      volume = {5},
      publisher = {Springer-Verlag},
      year = {1973},
      pages = {vii+217},
      mrclass = {12GXX (20F20 18H10)},
      mrnumber = {0404227},
      address = {New York},
      zblnumber = {0812.12002},
      }
  • [Steinberg] Go to document R. Steinberg, "Regular elements of semisimple algebraic groups," Publ. Math. Inst. Hautes Études Sci., vol. 25, pp. 49-80, 1965.
    @article{Steinberg, mrkey = {0180554},
      author = {Steinberg, Robert},
      title = {Regular elements of semisimple algebraic groups},
      journal = { Publ. Math. Inst. Hautes Études Sci.},
      fjournal = {Institut des Hautes Études Scientifiques. Publications Mathématiques},
      volume = {25},
      year = {1965},
      pages = {49--80},
      issn = {0073-8301},
      mrclass = {14.50 (20.75)},
      mrnumber = {0180554},
      mrreviewer = {J. L. Koszul},
      doi = {10.1007/BF02684397},
      zblnumber = {0136.30002},
      }
  • [SteinbergEndomorphisms] R. Steinberg, Endomorphisms of Linear Algebraic Groups, Providence, RI: Amer. Math. Soc., 1968, vol. 80.
    @book{SteinbergEndomorphisms, mrkey = {0230728},
      author = {Steinberg, Robert},
      title = {Endomorphisms of Linear Algebraic Groups},
      series = {Mem. Amer. Math. Soc.},
      volume = {80},
      publisher = {Amer. Math. Soc.},
      address = {Providence, RI},
      year = {1968},
      pages = {108},
      mrclass = {14.50 (22.00)},
      mrnumber = {0230728},
      mrreviewer = {E. Abe},
      zblnumber = {0164.02902},
      }
  • [T] D. Treumann, Smith theory and geometric Hecke algebras, 2011.
    @misc{T,
      author = {Treumann, D.},
      title = {Smith theory and geometric {H}ecke algebras},
      note = {preprint},
      arxiv = {1107.3798},
      year = {2011},
      }

Authors

David Treumann

Boston College, Chestnut Hill, MA

Akshay Venkatesh

Stanford University, Stanford, CA