Integral models for Shimura varieties of abelian type

Kisin, Mark^1, 2

¹Department of Mathematics, University of Chicago, Chicago, Illinois 60637
²Department of Mathematics, Harvard University, 1 Oxford Street, Cambridge, Massachusetts 02138

Journal of the American Mathematical Society, Tome 23 (2010) no. 4, pp. 967-1012

Résumé

We construct smooth integral models of Shimura varieties of abelian type at primes where the level structure is hyperspecial.

Détail

DOI : 10.1090/S0894-0347-10-00667-3

Bibliographie

[1] Blasius, Don A 𝑝-adic property of Hodge classes on abelian varieties 1994 293 308

[2] Berthelot, P., Ogus, A. 𝐹-isocrystals and de Rham cohomology. I Invent. Math. 1983 159 199

[3] Bruhat, F., Tits, J. Groupes réductifs sur un corps local. II. Schémas en groupes. Existence d’une donnée radicielle valuée Inst. Hautes Études Sci. Publ. Math. 1984 197 376

[4] Colliot-Thélène, J.-L., Sansuc, J.-J. Fibrés quadratiques et composantes connexes réelles Math. Ann. 1979 105 134

[5] Chevalley, Claude Deux théorèmes d’arithmétique J. Math. Soc. Japan 1951 36 44

[6] Colliot-Thélène, Jean-Louis, Suresh, Venapally Quelques questions d’approximation faible pour les tores algébriques Ann. Inst. Fourier (Grenoble) 2007 273 288

[7] Deligne, Pierre Travaux de Shimura 1971

[8] Deligne, Pierre, Milne, James S., Ogus, Arthur, Shih, Kuang-Yen Hodge cycles, motives, and Shimura varieties 1982

[9] Deligne, Pierre Variétés de Shimura: interprétation modulaire, et techniques de construction de modèles canoniques 1979 247 289

[10] Deligne, Pierre Équations différentielles à points singuliers réguliers 1970

[11] Schémas en groupes. I: Propriétés générales des schémas en groupes 1970

[12] Faltings, Gerd Integral crystalline cohomology over very ramified valuation rings J. Amer. Math. Soc. 1999 117 144

[13] Faltings, Gerd, Chai, Ching-Li Degeneration of abelian varieties 1990

[14] Fontaine, Jean-Marc Représentations 𝑝-adiques des corps locaux. I 1990 249 309

[15] Groupes de monodromie en géométrie algébrique. I 1972

[16] Kisin, Mark Crystalline representations and 𝐹-crystals 2006 459 496

[17] Kisin, Mark Potentially semi-stable deformation rings J. Amer. Math. Soc. 2008 513 546

[18] Kisin, Mark Modularity of 2-adic Barsotti-Tate representations Invent. Math. 2009 587 634

[19] Kisin, Mark Integral canonical models of Shimura varieties J. Théor. Nombres Bordeaux 2009 301 312

[20] Kottwitz, Robert E. Points on some Shimura varieties over finite fields J. Amer. Math. Soc. 1992 373 444

[21] Langlands, R. P. Some contemporary problems with origins in the Jugendtraum 1976 401 418

[22] Messing, William The crystals associated to Barsotti-Tate groups: with applications to abelian schemes 1972

[23] Mumford, D., Fogarty, J., Kirwan, F. Geometric invariant theory 1994

[24] Milne, James S. The points on a Shimura variety modulo a prime of good reduction 1992 151 253

[25] Milne, J. S. Canonical models of (mixed) Shimura varieties and automorphic vector bundles 1990 283 414

[26] Milne, J. S. Shimura varieties and motives 1994 447 523

[27] Moonen, Ben Models of Shimura varieties in mixed characteristics 1998 267 350

[28] Prasad, Gopal, Yu, Jiu-Kang On quasi-reductive group schemes J. Algebraic Geom. 2006 507 549

[29] Rapoport, M., Zink, Th. Period spaces for 𝑝-divisible groups 1996

[30] Saavedra Rivano, Neantro Catégories Tannakiennes 1972

[31] Springer, T. A. Reductive groups 1979 3 27

[32] Tits, J. Reductive groups over local fields 1979 29 69

[33] Vasiu, Adrian Integral canonical models of Shimura varieties of preabelian type Asian J. Math. 1999 401 518

[34] Waterhouse, William C. Introduction to affine group schemes 1979

[35] Zink, Thomas The display of a formal 𝑝-divisible group Astérisque 2002 127 248

[36] Zink, Thomas Windows for displays of 𝑝-divisible groups 2001 491 518