A guide to the reduction modulo p of Shimura varieties
Formes automorphes (I) - Actes du semestre du centre Émile Borel, printemps 2000, Astérisque, no. 298 (2005), p. 271-318
@incollection{AST_2005__298__271_0,
     author = {Rapoport, Michael},
     title = {A guide to the reduction modulo $p$ of Shimura varieties},
     booktitle = {Formes automorphes (I) - Actes du semestre du centre \'Emile Borel, printemps 2000},
     editor = {Tilouine Jacques and Carayol Henri and Harris Michael and Vign\'eras Marie-France},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {298},
     year = {2005},
     pages = {271-318},
     zbl = {1084.11029},
     mrnumber = {2141705},
     language = {en},
     url = {http://www.numdam.org/item/AST_2005__298__271_0}
}
Rapoport, Michael. A guide to the reduction modulo $p$ of Shimura varieties, in Formes automorphes (I) - Actes du semestre du centre Émile Borel, printemps 2000, Astérisque, no. 298 (2005), pp. 271-318. http://www.numdam.org/item/AST_2005__298__271_0/

[BD] A. Beilinson & V. Drinfeld - Quantization of Hitchhrs integrable system and Hecke eigensheaves, available at http://www.math.uchicago.edu/~benzvi/.

[BT1] F. Bruhat & J. Tits - Groupes réductifs sur un corps local, Publ. Math. Inst. Hautes Études Sci. 41 (1972), p. 5-251. | Article | Numdam | MR 327923 | Zbl 0254.14017

[BT2] F. Bruhat & J. Tits, Groupes réductifs sur un corps local. II Schémas en groupes. Existence d'une donnée radicielle valuée, Publ. Math. Inst. Hautes Études Sci. 60 (1984), p. 197-376. | Numdam | Numdam | MR 756316 | Zbl 0254.14017 | Zbl 0597.14041

[C1] C.-L. Chai - Every ordinary symplectic isogeny class in positive characteristic is dense in the moduli, Invent. Math. 121 (1995), p. 439-479. | Article | MR 1353306 | Zbl 0990.11039

[C2] C.-L. Chai, Newton polygons as lattice points, Amer. J. Math. 122 (2000), p. 967-990. | MR 1781927 | Zbl 1057.11506

[CN1] C.-L. Chai & P. Norman - Bad reduction of the Siegel moduli scheme of genus two with Γ 0 (p)-level structure, Amer. J. Math. 112 (1990), p. 1003-1071. | Article | MR 1081813 | Zbl 0734.14010

[CN2] C.-L. Chai & P. Norman, Singularities of the Γ 0 (p)-level structure, J. Algebraic Geom., 1 (1992), p. 251-278. | MR 1144439 | Zbl 0785.14001

[DL] P. Deligne & G. Lusztig - Representations of reductive groups over finite fields, Ann. of Math. 103 (1976), p. 103-161. | Article | MR 393266 | Zbl 0336.20029

[DP] P. Deligne & G. Pappas - Singularités des espaces de modules de Hilbert, en les caractéristiques divisant le discriminant, Compositio Math. 90 (1994), p. 59-79. | Numdam | MR 1266495 | Zbl 0826.14027

[DR] P. Deligne & M. Rapoport - Les schémas de modules de courbes elliptiques, in Modular functions of one variable, II (Proc. Internat. Summer School, Univ. Antwerp, Antwerp, 1972), Lect. Notes in Math., vol. 349, Springer, Berlin, 1973, p. 143-316. | Article | MR 337993 | Zbl 0281.14010

[DM] F. Digne & J. Michel - Representations of finite groups of Lie type, London Mathematical Society Student Texts, vol. 21, Cambridge University Press, Cambridge, 1991. | MR 1118841 | Zbl 0815.20014

[D] V. G. Drinfeld - Coverings of p-adic symmetric domains, Funktsional. Anal. i Prilozhen. 10 (1976), p. 29-40, Russian. | MR 422290 | Zbl 0346.14010

[F1] G. Faltings - Explicit resolution of local singularities of moduli-spaces. J. reine angew. Math. 483 (1997), p. 183-196. | MR 1431845 | Zbl 0871.14012

[F2] G. Faltings, Toroidal resolutions for some matrix singularities, in Moduli of abelian varieties (Texel Island, 1999), Progress in Math., vol. 195, Birkhäuser, Basel, 2001, p. 157-184. | Article | MR 1827019 | Zbl 1028.14002

[Ge] A. Genestier - Un modèle semi-stable de la variété de Siegel de genre 3 avec structures de niveau de type Γ 0 (p), Compositio Math. 123 (2000), p. 303-328. | Article | MR 1795293 | Zbl 0974.11029

[G1] U. Görtz - On the flatness of models of certain Shimura varieties of PEL-type, Math. Ann. 321 (2001), p. 689-727. | Article | MR 1871975 | Zbl 1073.14526

[G2] U. Görtz, On the flatness of local models for the symplectic group, Adv. in Math. 176 (2003), p. 89-115. | Article | MR 1978342 | Zbl 1051.14027

[G3] U. Görtz, Topological flatness of local models in the ramified case, math.AG/0205050, 2002. | Zbl 1085.14022

[H1] Th. Haines - On matrix coefficients of the Satake isomorphism: complements to the paper of M. Rapoport, Manuscripta Math. 101 (2000), p. 167-174. | Article | MR 1742250 | Zbl 0941.22007

[H2] Th. Haines, Test functions for Shimura varieties: the Drinfeld case, Duke Math. J. 106 (2001), p. 19-40. | Article | MR 1810365 | Zbl 1014.20002

[H3] Th. Haines, The combinatorics of Bernstein functions, Trans. Amer. Math. Soc. 353 (2001), p. 1251-1278. | Article | MR 1804418 | Zbl 0962.14018

[HN1] Th. Haines & B. C. Ngo - Alcoves associated to special fibers of local models, Amer. J. Math. 124 (2002), p. 1125-1152. | Article | MR 1939783 | Zbl 1047.20037

[HN2] Th. Haines & B. C. Ngo, Nearby cycles for local models of some Shimura varieties, Compositio Math. 133 (2002), p. 117-150. | Article | MR 1923579 | Zbl 1009.11042

[HR] Th. Haines & M. Rapoport - paper in preparation.

[IM] N. Iwahori & H. Matsumoto - On some Bruhat decomposition and the structure of the Hecke rings of p-adic Chevalley groups, Publ. Math. Inst. Hautes Etudes Sci. 25 (1965), p. 5-48. | Article | Numdam | MR 185016 | Zbl 0228.20015

[J] A. De Jong - The moduli spaces of principally polarized abelian varieties with Γ 0 (p)-level structure, J. Algebraic Geom. 2 (1993), p. 667-688. | MR 1227472 | Zbl 0816.14020

[JO] A. De Jong & F. Oort - Purity of the stratification by Newton polygons, J. Amer. Math. Soc. 13 (2000), p. 209-241. | Article | MR 1703336 | Zbl 0954.14007

[Ka] C. Kaiser - Ein getwistetes fundamentales Lemma für die GSp 4 , Bonner Mathematische Schriften, vol. 303, Universität Bonn, Mathematisches Institut, Bonn, 1997. | MR 1612837 | Zbl 0899.11025

[K1] R. Kottwitz - Shimura varieties and twisted orbital integrals, Math. Ann. 269 (1984), p. 287-300. | Article | MR 761308 | Zbl 0533.14009

[K2] R. Kottwitz, Isocrystals with additional structure, Compositio Math. 56 (1985), p. 201-220. | Numdam | MR 809866 | Zbl 0597.20038

[K3] R. Kottwitz, Points on some Shimura varieties over finite fields, J. Amer. Math. Soc. 5 (1992), p. 373-444. | Article | MR 1124982 | Zbl 0796.14014

[K4] R. Kottwitz, Isocrystals with additional structure. II, Compositio Math. 109 (1997), p. 255-339. | Article | MR 1485921 | Zbl 0966.20022

[KR1] R. Kottwitz & M. Rapoport - Minuscule alcoves for GL n and GSp 2n , Manuscripta Math. 102 (2000), p. 403-428. | Article | MR 1785323 | Zbl 0981.17003

[KR2] R. Kottwitz & M. Rapoport, On the existence of F-crystals, Comment. Math. Helv. 78 (2003), p. 153-184. | Article | MR 1966756 | Zbl 1126.14023

[L] L. Lafforgue - Pavages de polyèdres, recollement de cellules de Schubert et compactification d'espaces de configurations, in preparation.

[LR] R. Langlands & M. Rapoport - Shimuravarietäten und Gerben, J. reine angew. Math. 378 (1987), p. 113-220. | MR 895287 | Zbl 0615.14014

[LO] K.-Z. Li & F. Oort - Moduli of super singular abelian varieties, Lect. Notes in Math., vol. 1680, Springer-Verlag, Berlin, 1998. | MR 1611305 | Zbl 0920.14021

[M1] J. Milne - The conjecture of Langlands and Rapoport for Siegel modular varieties, Bull. Amer. Math. Soc. (N.S.) 24 (1991), p. 335-341. | Article | MR 1071030 | Zbl 0743.11031

[M2] J. Milne, The points on a Shimura variety modulo a prime of good reduction, in The zeta functions of Picard modular surfaces, Univ. Montréal, Montreal, QC, 1992, p. 151-253. | MR 1155229 | Zbl 0821.14016

[M3] J. Milne, Motives over finite fields, in Motives (Seattle, WA, 1991), Part 1, Proc. Sympos. Pure Math., vol. 55, American Mathematical Society, Providence, RI, 1994, p. 401-459. | MR 1265538 | Zbl 0811.14018

[NG] B. C. Ngo & A. Genestier - Alcoves et p-rang des variétés abéliennes, Ann. Inst. Fourier (Grenoble) 52 (2002), p. 1665-1680. | Article | Numdam | MR 1952527 | Zbl 1046.14023

[O] F. Oort - Newton polygon strata in the moduli space of abelian varieties, in Moduli of abelian varieties (Texel Island, 1999). Progress in Math., vol. 195, Birkhäuser, Basel, 2001, p. 417-440. | Article | MR 1827028 | Zbl 1086.14037

[P] G. Pappas - On the arithmetic moduli schemes of PEL Shimura varieties, J. Algebraic Geom. 9 (2000), p. 577-605. | MR 1752014 | Zbl 0978.14023

[PR1] G. Pappas & M. Rapoport - Local models in the ramified case I. The EL-case, J. Algebraic Geom. 12 (2003), p. 107-145. | Article | MR 1948687 | Zbl 1063.14029

[PR2] G. Pappas & M. Rapoport, Local models in the ramified case II. Splitting models, math.AG/0205021, 2002. | Zbl 1126.14028

[Pf] M. Pfau - The conjecture of Langlands and Rapoport for certain Shimura varieties of non-rational weight, J. reine angew. Math. 471 (1996), p. 165-199. | MR 1374922 | Zbl 0845.11024

[R1] M. Rapoport - On the local zeta function of quaternionic Shimura varieties with bad reduction, Math. Ann. 279 (1988), p. 673-697. | Article | MR 926427 | Zbl 0617.14017

[R2] M. Rapoport, On the bad reduction of Shimura varieties, in Automorphic forms, Shimura varieties, and L-functions, Vol. II (Ann Arbor, MI, 1988), Perspect. Math., vol. 11, Academic Press, Boston, MA, 1990, p. 253-321. | MR 1044832 | Zbl 0716.14010

[R3] M. Rapoport, A positivity property of the Satake isomorphism, Manuscripta Math. 101 (2000), p. 153-166. | Article | MR 1742251 | Zbl 0941.22006

[RR] M. Rapoport & M. Richartz - On the classification and specialization of F-isocrystals with additional structure, Compositio Math. 103 (1996), p. 153-181. | Numdam | MR 1411570 | Zbl 0874.14008

[RZ1] M. Rapoport & Th. Zink - Über die lokale Zetafunktion von Shimuravarietäten. Monodrorniefiltration und verschwindende Zyklen in ungleicher Charakteristik, Invent. Math. 68 (1982), p. 21-101. | Article | MR 666636 | Zbl 0498.14010

[RZ2] M. Rapoport & Th. Zink, Period spaces for p-divisible groups, Annals of Mathematics Studies, vol. 141, Princeton University Press, Princeton, NJ, 1996. | MR 1393439 | Zbl 0873.14039

[Re1] H. Reimann - The semi-simple zeta function of quaternionic Shimura varieties, Lect. Notes in Math., vol. 1657, Springer-Verlag, Berlin, 1997. | MR 1470457 | Zbl 1009.11044

[Re2] H. Reimann, On the zeta function of quaternionic Shimura varieties, Math. Ann. 317 (2000), p. 41-55. | Article | MR 1760668 | Zbl 1009.11045

[Re3] H. Reimann, Reduction of Shimura varieties at parahoric levels, Manuscripta Math. 107 (2002), p. 355-390. | Article | MR 1906202 | Zbl 1117.14026

[Ri] M. Richartz - Klassifikation von selbstdualen Dieudonnégittern in einem dreidimensionalen polarisierten supersingulären Isokristall, Diss., Universität Bonn, 1998. | MR 1936114 | Zbl 0906.14021

[S] H. Stamm - On the reduction of the Hilbert-Blumenthal-moduli scheme with Γ 0 (p)-level structure, Forum Math. 9 (1997), p. 405-455. | MR 1457134 | Zbl 0916.14022

[T] J. Tits - Reductive groups over local fields, Proc. Sympos. Pure Math., vol. 33, American Mathematical Society, Providence, RI, 1979, p. 29-69. | Article | MR 546588 | Zbl 0415.20035

[W] T. Wedhorn - Ordinariness in good reductions of Shimura varieties of PEL-type, Ann. scient. Éc. Norm. Sup. 4e série 32 (1999), p. 575-618. | Article | Numdam | MR 1710754 | Zbl 0983.14024

[BW] O. Bültel & T. Wedhorn - Congruence relations for Shimura varieties associated to some unitary groups, arXiv: math. AG/0202026, 2002. | MR 2225042 | Zbl 1124.11029

[FR] J.-M. Fontaine & M. Rapoport - Existence de filtrations admissibles sur des isocristaux, Bull. Soc. math. France, to appear; arXiv: math.NT/0204293. | Numdam | MR 2145020 | Zbl 1073.14025

[K5] R. Kottwitz - On the Hodge-Newton decomposition for split groups, Internat. Math. Res. Notices 26 (2003), p. 1433-1447. | Article | MR 1976046 | Zbl 1074.14016

[Le] C. Leigh - A converse to Mazur's inequality for split classical groups, arXiv: math. NT/0211327, 2002.

[R4] M. Rapoport - On the Newton stratification, in Séminaire Bourbaki 2001/2002, Astérisque, vol. 290, Société Mathématique de France, 2003, Exp. n° 903, p. 207-224. | Numdam | MR 2074057 | Zbl 1159.14304

[Reu1] D. Reuman - Determining whether certain affine Deligne-Lusztig sets are empty, arXiv: math.RT/0211434, 2002. | MR 2717068

[Reu2] D. Reuman, Formulas for the dimensions of some affine Deligne-Lusztig varieties, arXiv: math.RT/0303146, 2003. | MR 2069809 | Zbl 1053.22010

[Wi] J.-P. Wintenberger - Existence de F-cristaux avec structures supplémentaires, arXiv: math.NT/0303026, 2003. | MR 2104909 | Zbl 1104.14013