@book{AST_2004__291__R1_0, author = {Fargues, Laurent and Mantovan, Elena}, title = {Vari\'et\'es de {Shimura,} espaces de {Rapoport-Zink} et correspondances de {Langlands} locales}, series = {Ast\'erisque}, publisher = {Soci\'et\'e math\'ematique de France}, number = {291}, year = {2004}, zbl = {1050.11002}, language = {fr}, url = {http://www.numdam.org/item/AST_2004__291__R1_0/} }
TY - BOOK AU - Fargues, Laurent AU - Mantovan, Elena TI - Variétés de Shimura, espaces de Rapoport-Zink et correspondances de Langlands locales T3 - Astérisque PY - 2004 IS - 291 PB - Société mathématique de France UR - http://www.numdam.org/item/AST_2004__291__R1_0/ LA - fr ID - AST_2004__291__R1_0 ER -
Fargues, Laurent; Mantovan, Elena. Variétés de Shimura, espaces de Rapoport-Zink et correspondances de Langlands locales. Astérisque, no. 291 (2004), 343 p. http://numdam.org/item/AST_2004__291__R1_0/
[1] The geometry and cohomology of some simple Shimura varieties, Annals of Mathematics Studies, vol. 151, Princeton University Press, Princeton, NJ, 2001. | MR | Zbl
&[2] Points on some Shimura varieties over finite fields », J. Amer. Math. Soc 5 (1992), no. 2, p. 373-444. | MR | Zbl | DOI
«[3] Period spaces for -divisible groups, Annals of Mathematics Studies, no. 141, Princeton University Press, Princeton, NJ, 1996. | MR | Zbl
& -[1] Étale cohomology for non-Archimedean analytic spaces », Inst. Hautes Études Sci. Publ. Math 78 (1994), p. 5-161. | MR | Zbl | EuDML | Numdam | DOI
- «[2] Étale cohomology for -adic analytic spaces », Notes d'un exposé à Toulouse, Juin 1994.
, «[3] Vanishing cycles for formal schemes », Invent. Math. 115 (1994), no. 3, p. 539-571. | MR | Zbl | EuDML | DOI
, «[4] On the comparison theorem for étale cohomology of non-Archimedean analytic spaces », Israel J. Math 92 (1995), no. 1-3, p. 45-59. | MR | Zbl | DOI
, «[5] Vanishing cycles for formal schemes, II », Invent. Math. 125 (1996), no. 2, p. 367-390. | MR | Zbl | DOI
, «[6] Trace Paley Wiener theorem for reductive -adic groups », J. Analyse Math 47 (1986), p. 180-192. | MR | Zbl | DOI
, & - «[7] Théorie de Dieudonné cristalline, II, Lect. Notes in Math., vol. 930, Springer-Verlag, Berlin, 1982. | MR | Zbl
, & -[8] Mauvaise réduction des variétés de Drinfeld et correspondance de Langlands locale », Invent. Math 138 (1999), no. 3. p. 573-629. | MR | Zbl | DOI
- «[9] The admissible dual of via compact open sub-groups, Annals of Mathematics Studies, vol. 129, Princeton University Press, Princeton, NJ, 1993. | MR | Zbl
& -[10] Smooth representations of reductive -adic groups : structure theory via types », Proc. London Math. Soc 77 (1998). no. 3, p. 582-634. | Zbl | MR | DOI
& , - «[11] Non abelian Lubin-Tate theory », in Automorphic forms, Shimura varieties and -functions (Ann Arbor, MI, 1988), Perspect. Math., vol. 11, Academic Press, Boston, MA. 1990, p. 15-39. | MR | Zbl
- «[12] On limit multiplicities of discrete series representations in spaces of automorphic forms », Invent. Math 83 (1986), no. 2, p. 265-284. | MR | Zbl | EuDML | DOI
- «[13] The fundamental lemma for stable base change », Duke Math. J 61 (1990), no. 1, p. 255-302. | MR | Zbl | DOI
, «[14] Représentations galoisiennes associées aux représentations automorphes autoduales de ». Inst. Hautes Études Sci. Publ Math 73 (1991), p. 97-145. | MR | Zbl | EuDML | Numdam | DOI
, «[15] Théorie de Hodge. II », Inst. Hautes Études Sci. Publ. Math 40 (1971), p. 5-57. | MR | Zbl | EuDML | Numdam | DOI
- «[16] Travaux de Shimura », in Séminaire Bourbaki, 23ème année (1970/71), Lect. Notes in Math., vol. 244, Springer, Berlin, 1971, Exp. no. 389, p. 123-165. | MR | Zbl | EuDML | Numdam | DOI
, «[17] Le formalisme des cycles évanescents (exposés 13 et 14)», in SGA 7 II, Lect. Notes in Math., vol. 340, Springer-Verlag. 1973, p. 82-173. | Zbl
, «[18] Théorèmes de finitude en cohomologie -adique », in Séminaire de Géométrie Algébrique du Bois-Marie (SGA 4). Lect. Notes in Math., vol. 569, Springer-Verlag, 1977, avec la collaboration de J.F. Boutot, A. Grothendieck, L. Illusie et J.L. Verdier. | Zbl | MR
- «[19] Représentations des algèbres centrales simples -adiques, Travaux en Cours, Hermann, Paris, 1984. | MR | Zbl
, & -[20] Elliptic modules », Mat, Sb. (N.S.) 136 (1974), p. 594-627, 656. | MR | Zbl | EuDML
- «[21] Coverings of -adic symmetric domains », Funktional. Anal. i Priložen 10 (1976), no. 2, p. 29-40. | MR | Zbl
, «[22] On the adic formalism », in The Grothendieck Festschrift, Progress in Math., vol. 88, no. 2, Birkhäuser, Basel, Boston, 1990. | MR | Zbl
- «[23] Représentations -adiques potentiellement semi-stables », in Périodes -adiques, Astérisque, vol. 223, Société Mathématique de France, Paris, 1994, p. 321-347. | MR | Zbl | Numdam
- «[24] Étale cohomology and the Weil conjecture, Results in Mathematics and Related Areas (3), vol. 13, Springer-Verlag, Berlin-New York, 1988. | MR | Zbl
& -[25] Rigid geometry, Lefschetz-Verdier trace formula and Deligne's conjecture », Invent. math 127 (1997), p. 489-533. | MR | Zbl | DOI
- «[26] Discrete series characters and the Lefschetz formula for Hecke operators », Duke Math. J 89 (1997), no. 3, p. 477-554. | MR | Zbl | DOI
, & - «[27] Periods of integrals on algebraic manifolds. III. some global differential-geometric properties of the period mapping », Inst. Hautes Études Sci. Publ. Math 38 (1970), p. 125-180. | MR | Zbl | EuDML | Numdam | DOI
«[28] Formule de Lefschetz ». in SGA V. Lect. Notes in Math., vol. 589, Springer Verlag. 1977. p. 73-135. | Zbl
, & «[29] « The local Langlands correspondence », Notes of (half) a course at the IHP, Spring 2000, à paraître. | Zbl
-[30] Supercuspidal representations in the cohomology of Drinfel'd upper half spaces ; elaboration of Carayol's program », Invent. Math. 129 (1997). no. 1, p. 75-119. | MR | Zbl | DOI
, «[31] Galois properties of cohomological automorphic forms on ». J. Math. Kyoto Univ. 39 (1999). no. 1, p. 299-318. | MR | Zbl | DOI
, «[32] Local Langlands correspondences and vanishing cycles on Shimura varieties ». in Proceedings of the E.C.M., 2000.
, «[33] Conditional base change for unitary groups », Preprint. | MR | Zbl | DOI
& «[34] The geometry and cohomology of some simple Shimura varieties. Annals of Mathematics Studies, vol. 151. Princeton University Press, Princeton, NJ, 2001. | MR | Zbl
& -[35] Étale cohomology of rigid analytic varieties and adic spaces. Aspects of Mathematics., Friedr. Vieweg and Sohn, Braunschweig, 1996. | MR | Zbl
-[36] A comparison theorem for l-adic cohomology », Compositio Math., 112 (1998), no. 2. p. 217-235. | MR | Zbl | DOI
, «[37] A finiteness result for direct image sheaves on the étale site of rigid analytic varieties », J. Algebraic Geom 7 (1998), no. 2, p. 159-403. | MR | Zbl
, «[38] Swan representations associated with rigid analytic curves », J. Reine Angew. Math 537 (2001). p. 165-234. | MR | Zbl
, «[39] Complexe cotangent et déformations, I, Lect. Notes in Math., vol. 239, Springer-Verlag, Berlin-New York, 1971. | MR | Zbl
-[40] Complexe cotangent et déformations, II, Lect. Notes in Math., vol. 283, Springer-Verlag, Berlin-New York, 1972. | MR | Zbl
,[41] Autour du théorème de monodromie locale », in Périodes p-adiques. Astérisque, vol. 223. Société Mathématique de France, Paris, 1994. | MR | Zbl | Numdam
, «[42] Étale fundamental groups of non-archimedean analytic spaces », preprint. | MR | Zbl | Numdam
- «[43] Systèmes projectifs -adiques », in SGA V. Lect. Notes in Math., vol. 589, Springer Verlag, 1977. | Zbl
- «[44] Cuspidal geometry of -adic groups ». J. Analyse Math 47 (1986), p. 1-36. | MR | Zbl | DOI
- «[45] Hecke algebras of classical groups over -adic fields and supercuspidal representations », Amer. J. Math 121 (1999). no. 5, p. 967-1029. | MR | Zbl | DOI
- «[46] Rational conjugacy classes in reductive groups », Duke Math. J. 49 (1982). no. 1. p. 785-806. | MR | Zbl | DOI
- «[47] Isocrystals with additional structure », Compositio Math, 56 (1985), no. 2, p. 201-220. | MR | Zbl | EuDML | Numdam
, «[48] Stable trace formula : elliptic singular terms », Math. Ann 275 (1986), no. 3, p. 365-399. | MR | Zbl | EuDML | DOI
, «[49] Shimura varieties ans -adic representations », in Automorphie forms, Shimura varieties and L-functions (Ann Arbor. ML 1988), Perspect. Math., vol. 10, Academic Press, 1990, p. 161-209. | MR | Zbl
, «[50] On the -adic representations associated to some simple Shimura varieties ». Invent. Math, 108 (1992). no. 3. p. 653-665. | MR | Zbl | EuDML | DOI
, «[51] Points on some Shimura varieties over finite fields ». J. Amer. Math. Soc 5 (1992), no. 2, p. 373-441. | MR | Zbl | DOI
, «[52] Isocrystals with additional structure, II ». Compositio Math, 109 (1997), no. 3. p. 255-339. | MR | Zbl | DOI
, «[53] On the existence of -crystals », preprint. | MR | Zbl | DOI
& «[54] Fonctions élémentaires et lemme fondamental pour le changement de base stable ». Duke Math. J 61 (1990), no. 2. p. 519-530. | MR | Zbl
«[55] -indistinguishability for », Canad. J. Math 31 (1979), no. 1. p. 726-785. | MR | Zbl | DOI
& «[56] Automorphie representations, Shimura varieties, and motives. Ein Märchen », in Automorphic forms, representations and -functions (Oregon State Univ., Corvallis. Ore.). Proc. Sympos. Pure Math., vol. XXXIII, Amer. Math. Soc, Providence, R.I, 1979. | MR | Zbl
- «[57] The theory of commutative formal groups over fields of finite characteristic », Usp. Math. 18 (1963), p. 3-90. | MR | Zbl
- «The theory of commutative formal groups over Heids of finite characteristic », Russ. Math. Surveys, 18 (1963). p. 1-80. | Zbl | MR | DOI
- «[58] On certain unitary group Shimura varieties ». ce volume. | Zbl
- «[59] The crystals associated to Barsotti-Tate groups : with applications to abelian schemes, Lect. Notes in Math., vol. 264. Springer-Verlag. Berlin-New York, 1972. | MR | Zbl
-[60] Canonical models of (mixed) Shimura varieties and automorphic vector bundles », in Automorphic forms, Shimura varieties and -functions (Ann Arbor, MI, 1988), Perspect. Math., vol. 10. Academic Press. Boston, MA, 1990. | MR | Zbl
- «[61] The points on a Shimura variety modulo a prime of good reduction », in The Zeta functions of Picard modular surfaces, Univ. Montréal. Montreal, PQ, 1992. p. 151-253. | MR | Zbl
, «[62] Representations of over a -adic field », J. Reine Angew. Math 372 (1986), p. 178-208. | MR | Zbl | EuDML
- «[63] OVNIS et armes secrètes américaines : l'extraordinaire témoignage d'un scientifique, Albin Michel.
-[64] On the calculation of local terms in the Lefschetz-Verdier trace formula and its application to a conjecture of Deligne », Ann. of Math. 135 (1992), p. 483-525. | MR | Zbl | DOI
- «[65] Non-Archimedean period domains », in Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Zürich, 1994), Birkhäuser, 1995, p. 423-434. | MR | Zbl | DOI
- «[66] On the classification and specialization of -isocrystals with additional structure », Compositio Math. 103 (1996), no. 2, p. 153-181. | MR | Zbl | EuDML | Numdam
& «[67] Über die lokale Zetafunktion von Shimuravarietäten. Monodromiefiltration und verschwindende Zyklen in ungleicher Charakteristik », Invent. Math 68 (1982), no. 1, p. 21-101. | MR | Zbl | EuDML | DOI
& - «[68] Period spaces for -divisible groups, Annals of Mathematics Studies, no. 141, Princeton University Press, Princeton, NJ, 1996. | MR | Zbl
& ,[69] Automorphic representations of unitary groups in three variables. Annals of Mathematics Studies, vol. 123, Princeton University Press, Princeton, NJ, 1990. | MR | Zbl
-[70] Analytic expression for the number of points mod », in The Zeta functions of Picard modular surfaces, Univ. Montréal, Montreal, QC, 1992, p. 65-109. | MR | Zbl
, «[71] The multiplicity formula for -packets », in The Zeta functions of Picard modular surfaces. Univ. Montréal, Montreal, QC, 1992, p. 395-419. | MR | Zbl
, «[72] Representation theory and sheaves on the Bruhat-Tits building », Inst. Hautes Études Sci. Publ. Math. 85 (1997), p. 97-191. | MR | Zbl | EuDML | Numdam | DOI
& «[73] On the Jacquet-Langlands correspondance in the cohomology of Lubin-Tate deformation tower », Preprint.
«[74] Ordinariness in good reductions of Shimura varieties of -type », Ann. Sci. École Norm, Sup 32 (1999), no. 5, p. 575-618. | MR | Zbl | EuDML | Numdam | DOI
- «[75] Propriétés du groupe tannakien des structures de Hodge -adiques et torseur entre cohomologies cristalline et étale », Ann. Inst, Fourier 47 (1997), no. 5. p. 1289-1334. | MR | Zbl | EuDML | Numdam | DOI
- «[76] The Lefschetz trace formula for an open algebraic surface », in Automorphic forms, Shimura varieties and -functions (Ann Arbor, MI, 1988), Perspect. Math., vol. 11, Academic Press, Boston, MA, 1990. | MR | Zbl
- «[77] On the slope filtration ». Duke Math. J 109 (2001), no. 1, p. 79-95. | MR | Zbl | DOI
, «[1] Théorie des topos et cohomologie étale des schémas. Séminaire de Géométrie Algébrique du Bois-Marie 1963-1964 (SGA 4), Lect. Notes in Math., vol. 269, 270, 305, Springer-Verlag, Berlin-New York, 1972, avec la collaboration de N. Bourbaki. P. Deligne et B. Saint-Donat. | Zbl
, & (eds.) -[2] Étale cohomology for non-Archimedean analytic spaces, Inst. Hautes Études Sci. Publ. Math 78 (1994). p. 5-161. | Zbl | MR | EuDML | Numdam | DOI
-[3] Vanishing cycles for formal schemes. Invent. Math. 115 (1994). no. 3. p. 539-571. | MR | Zbl | EuDML | DOI
,[4] Vanishing cycles for formal schemes. II. Invent. Math. 125 (1996), no. 2, p. 367-390. | MR | Zbl | DOI
,[5] Representations of -adic groups: a survey, in Automorphic forms, representations and -functions (Oregon State Univ., Corvallis. Ore., 1977), Proc. Sympos. Pure Math., vol. XXXIII. Amer. Math. Soc., Providence. R.I, 1979. p. 111-155. | MR | Zbl | DOI
-[6] Modular curves, descent theory, and rigid analytic spaces, in preparation.
-[7] Cohomolgie étale, in Séminaire de Géométrie Algébrique du Bois-Marie (SGA 4), Lect. Notes in Math., vol. 569. Springer-Verlag, Berlin-New York, 1977, avec la collaboration de J.F. Boutot. A. Grothendieck. L. Illusie et J.L. Verdier. | MR | Zbl
-[8] Représentations des algèbres centrales simples -adiques. Travaux en Cours. Hermann, Paris, 1984. | MR | Zbl
, &. -[9] Elliptic modules. Mat, Sb. (N.S.) 136 (1974), p. 594 627, 656. | MR | Zbl | EuDML
-[10] Cohomologie d'espaces de modules de groupes -divisibles et correspondances de Langlands locales, ce volume. | Zbl
-[11] Étale cohomology and the Weil conjecture, Results in Mathematics and Related Areas (3). vol. 13. Springer-Verlag, Berlin-New York, 1988. | MR | Zbl
& -[12] Séminaire de Géométrie Algébrique. I. Revêtements étales et Groupes Fondamental, Lect. Notes in Math., vol. 224, Springer, Berlin-Heidelberg-New York, 1971. | MR
-[13] Groupes de Barsotti-Tate et cristaux de Dieudonné. Sém. Math. Sup. Univ. Montréal, Presses Univ. Montréal, 1974. | MR | Zbl
,[14] The geometry and cohomology of some simple Shimura varieties. Annals of Mathematics Studies, vol. 151. Princeton University Press, Princeton, NJ. 2001. | MR | Zbl
&[15] Algebraic geometry, Graduate Texts in Math., vol. 52, Springer-Verlag. New York-Heidelberg, 1977. | MR | Zbl
-[16] Kroneckerian model of fields of elliptic modular functions, Amer. J. Math. 81 (1959), p. 561-577. | MR | Zbl | DOI
-[17] Déformations de groupes de Barsotti-Tate (d'après A. Grothendieck), in Seminar on Arithmetic bundles: the Mordell conjecture (Paris. 1983/84). Astérisque, vol. 127. Société Mathématique de France, Paris, 1985. p. 151-198. | MR | Zbl | Numdam
-[18] Purity of the stratification by Newton polygons, J. Amer. Math. Soc. 13 (2000). no. 1, p. 209-241. | MR | Zbl | DOI
& -[19] Slope Filtration of -crystals, in Journées de Géométrie Algébrique de Rennes (Rennes, 1978). Astérisque, vol. 63. Société Mathématique de France, Paris, 1979, p. 113-163. | MR | Numdam | Zbl
-[20] Arithmetic moduli of elliptic curves. Annals of Mathematics Studies, vol. 108, Princeton University Press, Princeton, NJ. 1985. | MR | Zbl
& -[21] Shimura varieties ans -adic representations, in Automorphic forms, Shimura varieties and -functions (Ann Arbor, MI, 1988), Perspect. Math., vol. 10, Academic Press, 1990, p. 161-209. | MR | Zbl
-[22] Points on some Shimura varieties over finite fields. J. Amer. Math, Soc 5 (1992), no. 2, p. 373-444. | MR | Zbl | DOI
,[23] Foliations in moduli spaces of abelian varieties, in preparation. | Zbl
-[24] Moduli of abelian varieties and Newton polygons, C. R. Acad, Sci. Paris Sér. I Math, 312 (1991), no. 5, p. 385-389. | MR | Zbl
,[25] Families of -divisible groups with constant Newton polygon, to appear. | MR | Zbl
& -[26] Non-Archimedean period domains, in Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Zurich, 1994), Birkhäuser, 1995, p. 423-434. | MR | Zbl | DOI
-[27] Period spaces for -divisible groups, Annals of Mathematics Studies, no. 141, Princeton University Press, Princeton, NJ, 1996. | MR | Zbl
& -[28] On Oort's foliation, Handwritten notes of F. Oort's talk in Essen.
-[29] On the slope filtration, Duke Math. J 109 (2001). no. 1, p. 79-95 | MR | Zbl | DOI
,