p-adic uniformization of unitary Shimura varieties
Varshavsky, Yakov
Publications Mathématiques de l'IHÉS, Tome S88 (1998), p. 57-119 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 1998-01-01
@article{PMIHES_1998__87__57_0,
     author = {Varshavsky, Yakov},
     title = {$p$-adic uniformization of unitary Shimura varieties},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     volume = {S88},
     year = {1998},
     pages = {57-119},
     mrnumber = {99m:14045},
     zbl = {0993.14008},
     language = {en},
     url = {http://dml.mathdoc.fr/item/PMIHES_1998__87__57_0}
}

Varshavsky, Yakov. $p$-adic uniformization of unitary Shimura varieties. Publications Mathématiques de l'IHÉS, Tome S88 (1998) pp. 57-119. http://gdmltest.u-ga.fr/item/PMIHES_1998__87__57_0/

[BC] J.-F. Boutot et H. Carayol, Uniformisation p-adique des courbes de Shimura : les théorèmes de Cherednik et de Drinfel'd, Astérisque 196-197 (1991), 45-156. | Zbl 0781.14010

[Be1] V. G. Berkovich, Spectral Theory and Analytic Geometry over Non-Archimedean Fields, American Mathematical Society, Providence, Rhode Island, 1990. | MR 91k:32038 | Zbl 0715.14013

[Be2] V. G. Berkovich, The Automorphism Group of the Drinfeld Half-Plane, C.-R. Acad. Sci. Paris, Ser. I Math. 321 (1995), 1127-1132. | MR 96h:11053 | Zbl 0856.14007

[Be3] V. G. Berkovich, Étale Cohomology for Non-Archimedean Analytic Spaces, Publ. Math. IHES 78 (1993), 5-161. | Numdam | MR 95c:14017 | Zbl 0804.32019

[Bo] A. Borel, Linear Algebraic Groups, Springer, 1991. | MR 92d:20001 | Zbl 0726.20030

[Br] K. S. Brown, Buildings, Springer, 1989. | MR 90e:20001 | Zbl 0715.20017

[BT] R. Bott and L. W. Tu, Differential Forms in Algebraic Topology, Springer, 1982. | MR 83i:57016 | Zbl 0496.55001

[CF] J. W. S. Cassels and A. Frölich (eds.), Algebraic Number Theory, Academic Press, 1967. | Zbl 0153.07403

[Ch1] I. V. Cherednik, Towers of Algebraic Curves Uniformized by Discrete Subgroups of PGL2 (Kw) X E, Math. USSR Sbornik 28 (1976), 187-215. | Zbl 0369.14013

[Ch2] I. V. Cherednik, Uniformization of Algebraic Curves by Discrete Arithmetic Subgroups of PGL2(Kw) with Compact Quotients, Math. USSR Sbornik 29 (1976), 55-85. | Zbl 0379.14010

[C1] L. Clozel, Représentations galoisiennes associées aux représentations automorphes autoduales de GL(n), Publ. Math. IHES 73 (1991), 77-145. | Numdam | MR 92i:11055 | Zbl 0739.11020

[De1] P. Deligne, Travaux de Shimura, Sem. Bourbaki 389, Lecture Notes in Math. 244, Springer, 1971. | Numdam | MR 58 #16675 | Zbl 0225.14007

[De2] P. Deligne, Variétés de Shimura : interprétation modulaire et techniques de construction de modèles canoniques, Proc. Symp. Pur. Math. 33, Part II, Amer. Math. Soc. (1979), 247-290. | MR 81i:10032 | Zbl 0437.14012

[DM] P. Deligne and J. Milne, Tannakian Categories, in Hodge Cycles, Motives and Shimura varieties, Lecture Notes in Math. 900, Springer, 1982, 101-228. | MR 84m:14046 | Zbl 0477.14004

[Dr1] V. G. Drinfel'D, Elliptic Modules, Math. USSR Sbornik 23 (1974), 561-592. | MR 52 #5580 | Zbl 0321.14014

[Dr2] V. G. Drinfel'D, Coverings of p-Adic Symmetric Regions, Functional Anal. Appl. 10 (1976), 107-115. | MR 54 #10281 | Zbl 0346.14010

[Ha] R. Hartshorne, Algebraic Geometry, Springer, 1977. | MR 57 #3116 | Zbl 0367.14001

[He] S. Helgason, Differential Geometry and Symmetric Spaces, Academic Press, 1962. | MR 26 #2986 | Zbl 0111.18101

[Ih] Y. Ihara, On Congruence Monodromy Problems, Lecture Notes at Univ. Tokyo 1 (1968), 2 (1969). | MR 44 #6706 | Zbl 0228.14010 | Zbl 0228.14009

[Ko] R. E. Kottwitz, Tamagawa Numbers, Ann. of Math. 127 (1988), 629-646. | MR 90e:11075 | Zbl 0678.22012

[Ku] A. Kurihara, Construction of p-Adic Unit Balls and the Hirzebruch Proportionality, Amer. J. Math. 102 (1980), 565-648. | MR 82e:10054 | Zbl 0498.14011

[La] S. Lang, Algebraic Number Theory, Addison-Wesley, 1970. | MR 44 #181 | Zbl 0211.38404

[Ma] G. A. Margulis, Discrete Subgroups of Semisimple Lie Groups, Springer-Verlag, 1991. | MR 92h:22021 | Zbl 0732.22008

[Mi1] J. Milne, Canonical Models of (Mixed) Shimura Varieties, in Automorphic forms, Shimura Varieties and L-functions, Vol. 1, CLOZEL and J. MILNE (eds.), Academic Press (1990), 283-414. | MR 91a:11027 | Zbl 0704.14016

[Mi2] J. Milne, Étale Cohomology, Princeton Univ. Press, 1980. | MR 81j:14002 | Zbl 0433.14012

[Mi3] J. Milne, The Points on a Shimura Variety Modulo a Prime of Good Reduction, in Zeta Functions of Picard Modular Surfaces, R. LANGLANDS and D. RAMAKRISHNAN (eds.), Univ. Montreal (1992), 151-253. | MR 94g:11041 | Zbl 0821.14016

[Mum1] D. Mumford, An Analytic Construction of Degenerating Curves over Complete Local Rings, Compositio Math. 24 (1972), 129-174. | Numdam | MR 50 #4592 | Zbl 0228.14011

[Mum2] D. Mumford, Abelian Varieties, Oxford Univ. Press, 1970. | MR 44 #219 | Zbl 0223.14022

[Mus] G. A. Mustafin, Nonarchimedean Uniformization, Math. USSR Sbornik 34 (1978), 187-214. | Zbl 0411.14006

[PR] V. Platonov and A. Rapinchuk, Algebraic Groups and Number Theory, Academic Press, 1994. | MR 95b:11039 | Zbl 0841.20046

[Ra] M. Rapoport, On the Bad Reduction of Shimura Varieties, in Automorphic Forms, Shimura Varieties and L-Functions, Vol. 2, L. CLOZEL and J. MILNE (eds.), Academic Press (1990), 253-321. | MR 91g:11065 | Zbl 0716.14010

[RZ1] M. Rapoport and Th. Zink, Über die Lokale Zetafunktion von Shimura Varietäten, Invent. Math. 68 (1982), 21-101. | Zbl 0498.14010

[RZ2] M. Rapoport and Th. Zink, Period Spaces for p-Divisible Groups, Annals of Math. Studies 141, Princeton University Press, 1996. | MR 97f:14023 | Zbl 0873.14039

[Ru] W. Rudin, Function Theory in the Unit Ball of Cn, Springer, 1980. | MR 82i:32002 | Zbl 0495.32001

[Sc] W. Scharlau, Quadratic and Hermitian Forms, Springer-Verlag, 1985. | MR 86k:11022 | Zbl 0584.10010

[SGA1] A. Grothendieck, Séminaire de Géométrie algébrique I, Revêtements étales et groupes fondamental, Lecture Notes in Math. 224, Springer, 1971. | MR 50 #7129 | Zbl 0234.14002

[Sha] I. R. Shafarevich, Basic Algebraic Geometry, Springer, 1974. | MR 51 #3163 | Zbl 0284.14001

[Shi] G. Shimura, Introduction to the Arithmetic Theory of Automorphic Functions, Princeton, Princeton Univ. Press, 1971. | Zbl 0221.10029

[Se1] J.-P. Serre, Géométrie algébrique et géométrie analytique, Ann. Inst. Fourier 6 (1956), 1-42. | Numdam | MR 18,511a | Zbl 0075.30401

[Se2] J.-P. Serre, Cohomologie des groupes discrets, in Prospects in Mathematics, Ann. of Math. Studies 70, Princeton Univ. Press (1971), 77-169. | MR 52 #5876 | Zbl 0235.22020

[St] S. Sternberg, Lectures on Differential Geometry, Prentice Hall, Inc. Englewood Cliffs, NJ, 1964. | MR 33 #1797 | Zbl 0129.13102

[Ti] J. Tits, Classification of Algebraic Semisimple Groups, Proc. Symp. Pure Math. 9, Amer. Math. Soc. (1966), 32-62. | MR 37 #309 | Zbl 0238.20052

[Va] Y. Varshavsky, p-Adic Uniformization of Unitary Shimura Varieties II, to appear in the Journal of Diff. Geom. | Zbl 0923.11092

[Wa] B. L. Van Der Waerden, Modern Algebra, Frederick Ungar Publishing CO, 1950. | MR 12,236f | Zbl 0039.00902

[We1] A. Weil, Adèles and Algebraic Groups, Progress in Math. 23, Birkhäuser, 1982. | MR 83m:10032 | Zbl 0493.14028

[We2] A. Weil, Basic Number Theory, Springer, 1967. | MR 38 #3244 | Zbl 0176.33601

[Ya] S.-T. Yau, Calabi's Conjecture and Some Results in Algebraic Geometry, Proc. Nat. Acad. Sci. USA 74 (1977), 1798-1799. | MR 56 #9467 | Zbl 0355.32028