@incollection{AST_2002__280__1_0,
author = {Mokrane, Abdellah and Tilouine, Jacques},
title = {Cohomology of {Siegel} varieties with $p$-adic integral coefficients and applications},
booktitle = {Cohomology of Siegel varieties},
editor = {Mokrane, Abdellah and Polo, Patrick and Tilouine, Jacques},
series = {Ast\'erisque},
pages = {1--95},
year = {2002},
publisher = {Soci\'et\'e math\'ematique de France},
number = {280},
mrnumber = {1944174},
zbl = {1078.11037},
language = {en},
url = {https://www.numdam.org/item/AST_2002__280__1_0/}
}
TY - CHAP AU - Mokrane, Abdellah AU - Tilouine, Jacques TI - Cohomology of Siegel varieties with $p$-adic integral coefficients and applications BT - Cohomology of Siegel varieties AU - Collectif ED - Mokrane, Abdellah ED - Polo, Patrick ED - Tilouine, Jacques T3 - Astérisque PY - 2002 SP - 1 EP - 95 IS - 280 PB - Société mathématique de France UR - https://www.numdam.org/item/AST_2002__280__1_0/ LA - en ID - AST_2002__280__1_0 ER -
%0 Book Section %A Mokrane, Abdellah %A Tilouine, Jacques %T Cohomology of Siegel varieties with $p$-adic integral coefficients and applications %B Cohomology of Siegel varieties %A Collectif %E Mokrane, Abdellah %E Polo, Patrick %E Tilouine, Jacques %S Astérisque %D 2002 %P 1-95 %N 280 %I Société mathématique de France %U https://www.numdam.org/item/AST_2002__280__1_0/ %G en %F AST_2002__280__1_0
Mokrane, Abdellah; Tilouine, Jacques. Cohomology of Siegel varieties with $p$-adic integral coefficients and applications, dans Cohomology of Siegel varieties, Astérisque, no. 280 (2002), pp. 1-95. https://www.numdam.org/item/AST_2002__280__1_0/
[1] , , , : Smooth compactification of locally symmetric varieties, Math. Sci. Press., Brookline, 1975. | MR | Zbl
[2] , , : Faisceaux pervers, Astérisque 100 (1982). | MR | Zbl | Numdam
[3] , , : Differential operators on the base affine space and a study of the -modules, in Lie Groups and their Representations, ed. I.M. Gelfand, Proc. Conf. Budapest 1971, Adam Hilger Publ., London, 1975. | MR | Zbl
[4] , : Notes on crystalline cohomology, P.U.P., Princeton, 1978. | MR | Zbl
[5] : Stable real cohomology of arithmetic groups, Ann. Sci. Éc. Norm. Sup. (4) 7 (1974) 235-272. | MR | Zbl | EuDML | Numdam | DOI
[6] : Stable and -cohomology of arithmetic groups, Bull. Am. Math. Soc., (N.S.) 3, (1980), 1025-1027. | MR | Zbl | DOI
[7] : Regularization theorems in Lie algebra cohomology, applications, Duke Math. J. 50 (1983), 605-623. | MR | Zbl | DOI
[8] , : Continuous cohomology, discrete subgroups, and representations of reductive groups, P.U.P. 1980. | MR | Zbl
[9] , , : Coherent cohomology, limits of discrete series and Galois conjugation, Duke Math. J. 73, 1994, 647-684. | MR | Zbl
[10] , : Motives for Hilbert modular forms, Inv. Math. 114, (1993) 55-87. | MR | Zbl | EuDML | DOI
[11] : Une remarque sur les représentations locales -adiques et les congruences entre formes modulaires de Hilbert, Bull. Soc. Math. France 127 (1999), no. 3, 459-472. | MR | Zbl | EuDML | Numdam | DOI
[12] : Groupes et Algèbres de Lie, Chap. 7, 8, Hermann 1975. | Zbl
[13] , : Degeneration of Abelian Varieties, Erg. Math. Wiss. 3. folge, 22, Springer Verlag, 1990. | MR | Zbl
[14] : Motifs et formes automorphes: application du principe de fonctorialité, in Proc. Ann Arbor Conf. (Automorphic Forms, Shimura Varieties and -functions, vol. I and II, Eds. L. Clozel, J.S. Milne), vol. I, 77-159., Persp. in Math., Acad. Press 1990. | MR | Zbl
[15] : Travaux de Griffiths, Sém. Bourbaki exp. 376, LN 180, Springer Verlag 1972. | Zbl | Numdam
[16] : The Taylor-Wiles construction and multiplicity one, Inv. Math. 128, (1997) 379-391. | MR | Zbl | DOI
[17] , : Schémas en groupes III (SGA 3, 1962/64), Springer Lect. Notes 153, Springer Verlag, 1970. | Zbl | MR
[18] : Formes quadratiques et groupes classiques, PUF, Paris 1981. | MR | Zbl
[19] : Valeur critique de la fonction adjointe d'une forme modulaire de Hilbert et arithmétique du motif correspondant, thèse Paris 13, 2003.
[20] : Complexe dualisant et applications à la classe fondamentale d'un cycle, Mémoire de la SMF 58, 1978. | MR | Zbl | EuDML | Numdam
[21] : On the cohomology of locally symmetric hermitian spaces, in Séminaire d'Algèbre, pp. 349-366, Springer Lecture Notes 1029, 1983. | MR | Zbl
[22] : Crystalline cohomology and -adic Galois representations, in Algebraic Analysis, ed. J.-I. Igusa, Proc JAMI inaugural Conference, the Johns Hopkins Univ. Press, 1990. | Zbl | MR
[23] : -isocrystals on open varieties. Results and conjectures, in Grothendieck's Festschrift, Birkhäuser, 1990, Boston. pp. 219-248. | MR | Zbl
[24] , : Construction de représentations -adiques, Ann. Sci. Éc. Norm. Sup. (4), 15 (1982) 547-608. | MR | Zbl | EuDML | Numdam | DOI
[25] : Harmonic analysis in weighted -spaces, Ann. Sci. Éc. Norm. Sup. (4), 31 (1998) 181-279. | MR | Zbl | EuDML | Numdam | DOI
[26] : Siegelsche Modulfunktionen, Grundl. Math. Wiss. 254, Springer Verlag 1983. | MR | Zbl
[27] , : Etale cohomology and the Weil Conjecture, Springer Verlag 1988. | MR | Zbl | DOI
[28] : Level optimization in the totally real case, preprint 1999.
[29] : Deformation rings and Hecke algebras in the totally real case, version 2.0, preprint 1999.
[30] : Arithmetical compactifications of Shimura varieties, preprint.
[31] : Intersection Theory, Erg. Math., Springer Verlag 1984. | MR | Zbl
[32] , : Representation Theory, Springer Verlag 1991. | MR | Zbl
[33] , : Eléments de Géométrie Algébrique IV, Etude locale des schémas et des morphismes de schémas (seconde partie), Pub. Math. IHES 24 (1965). | MR | Zbl | EuDML | Numdam
[34] : unpublished notes, 1992.
[35] : Eisensteinkohomologie und die Konstruktion gemischter motive, SLN 1562, Springer Verlag 1993. | MR | Zbl
[36] : Automorphic forms of -cohomology as coherent cohomology classes, J. Diff. Geom. 32, (1990) 1-63. | MR | Zbl | DOI
[37] : Functorial properties of toroidal compactifications of locally symmetric varieties, Proc. London Math. Soc 59, (1989) 1-22. | MR | Zbl | DOI
[38] , : Deformations of automorphic Galois representations, preprint 1998.
[39] , : Boundary Cohomology of Shimura varieties: Eisenstein classes in coherent cohomology, Ann. Sci. Éc. Norm. Sup. (4), 27 (1994), no. 3, 249-344. | MR | Zbl | EuDML | Numdam | DOI
[40] : On -adic Hecke algebras for over totally real fields, Ann. of Math. 128 (1988), 295-384. | MR | Zbl | DOI
[41] : Nearly ordinary Hecke algebras and Galois representations of several variables, in Algebraic Analysis, ed. J.-I. Igusa, Proc JAMI inaugural Conference, the Johns Hopkins Univ. Press, 1990. | Zbl | MR
[42] : Control Theorems of -nearly Ordinary Cohomology Groups, Bull. Soc. Math. France 123, (1995) 425-475. | Zbl | MR | EuDML | Numdam | DOI
[43] : Control theorems for coherent sheaves on Shimura varieties of type, preprint. | MR | Zbl | DOI
[44] : Réduction semi-stable et décomposition de complexes de de Rham à coefficients, Duke Math. J. 60, (1990) 139-185. | MR | Zbl
[45] : Cohomologie de de Rham et cohomologie étale -adique (d'après G. Faltings, J.-M. Fontaine et al.), Séminaire Bourbaki, Exp. No. 726, vol. 1989/90 Astérisque No. 189-190, (1990) 325-374. | MR | EuDML | Numdam | Zbl
[46] : Representations of algebraic groups, Acad. Press, 1987. | MR | Zbl
[47] : letter to the authors, May 11, 1998.
[48] : Logarithmic structures of Fontaine-Illusie, Algebraic Analysis, ed. J.-I. Igusa, Proc JAMI inaugural Conference, the Johns Hopkins Univ. Press, 1990. | MR | Zbl
[49] : Nilpotent connections and the monodromy theorem: applications of a result of Turrittin, Publ. Math. I.H.E.S. 39 (1971), 175-232. | MR | Zbl | EuDML | Numdam | DOI
[50] , : Some consequences of the Riemann hypothesis for varieties over finite fields, Inv. Math. 23, (1974) 73-77. | MR | Zbl | EuDML | DOI
[51] : The Standard Conjectures, p. 3-20, in Motives, vol. I, PSPM 55, AMS 1994. | MR | Zbl | DOI
[52] : Sur la cohomologie à supports compacts des variétés de Shimura pour , Comp. Math. 105, (1996) 267-359. | MR | Zbl | DOI
[53] : Fonctions zeta des variétés de Siegel de dimension trois, to appear.
[54] , : Représentations galoisiennes, différentielles de Kähler et conjectures principales, Publ. Math. IHES 71, 1990. | MR | Zbl | EuDML | Numdam | DOI
[55] : Abelian Varieties, Oxford Univ. Press 1970. | MR | Zbl
[56] : Hirzebruch's proportionality theorem in the non-compact case, Inv. Math. 42 (1977), 239-272. | MR | Zbl | EuDML | DOI
[57] : Cohomologie cristalline des variétés ouvertes, Maghreb Math. Rev., 2, (1993) 161-175. | MR
[58] : Arithmetical compactification of mixed Shimura varieties, Dissertation, Bonn 1989. | MR | Zbl
[59] : On -adic sheaves on Shimura varieties and their higher direct images in the Baily-Borel compactification, Math. Ann. 292, (1992) 197-240. | MR | Zbl | EuDML | DOI
[60] : Representations -adiques ordinaires, in Périodes -adiques, Astérisque 223, 1994. | MR | Zbl | Numdam
[61] , : Bernstein-Gelfand-Gelfand complexes and cohomology of nilpotent groups over , this volume. | Zbl | Numdam
[62] : On -adic representations attached to modular forms, Inv. Math. 28 (1975) 245-275. | MR | Zbl | EuDML | DOI
[63] : Non-vanishing of global theta-lifts from orthogonal groups, preprint, 1999. | MR | Zbl
[64] : letter to the authors, 21/07/99.
[65] : Global -packets for and theta lifts, Documenta Mathematica, 6 (2001), 247-314. | MR | Zbl | EuDML
[66] : Hilbert modular forms and p-adic Hodge theory, preprint, April 1999. | MR | Zbl
[67] : On Euler products and residual Eisenstein cohomology classes for Siegel modular varieties, Forum Math. 7 (1995), 1-28. | MR | Zbl | EuDML | DOI
[68] : A reciprocity law in non-solvable extensions, J. reine ang. Math., 221 (1966), 209-220. | MR | Zbl | EuDML
[69] : On the Eisenstein series of Hilbert Modular Groups, Rev. Matematica Iberoamericana, 1, (1985) no. 3, 1-42. | MR | Zbl | EuDML
[70] : Reductive groups, in Automorphic Forms, Representations, and Lfunctions, Corvallis, PSPM XXXIII, t. 1, AMS 1979. | MR | Zbl | DOI
[71] : Galois representations associated to Siegel modular forms of low weight, Duke Math. J. 63, (1991) 281-332. | MR | Zbl
[72] : On the -adic cohomology of Siegel threefolds, Inv. Math. 114, (1993) 289-310. | MR | Zbl | EuDML | DOI
[73] , : Ring-theoretic properties of certain Hecke algebras, Ann. Math. 141, (1995) 553-572. | MR | Zbl | DOI
[74] SGA4: , , : Théorie des topos et cohomologie étale des schémas, Lect. Notes in Math. 305, Springer Verlag 1972-73. | Zbl | MR
[75] SGA41/2: : Cohomologie Étale, Lect. Notes in Math. 569, Springer Verlag 1977. | MR | Zbl
[76] : Deformations of Galois representations and Hecke algebras, Narosa Publ., New Delhi 1996. | MR | Zbl
[77] , : Several variable -adic families of Siegel-Hilbert cusp eigensystems and their Galois representations, Ann. Sci. Ec. Norm. Sup. (4), 32, (1999) 499-574. | MR | Zbl | EuDML | Numdam | DOI
[78] : Syntomic complexes and -adic vanishing cycles, J. reine angew. Math. 472, (1996) 69-138. | MR | Zbl | EuDML
[79] : On the torsion of the cohomology of the Siegel threefold, preprint 1998.
[80] : Sur les représentations -adiques associées aux représentations cuspidales de , preprint 1998.
[81] : Correspondances entre représentations automorphes de sur une extension quadratique et sur , Conjecture locale de Langlands pour in Proc. Bowdoin Conf. (1984): "The Selberg Trace Formula and Related Topics", eds. D. Hejhal, P. Sarnak, A. Terras, Cont. Math. Ser. 53, 1986, AMS Publ., Providence RI. | MR | Zbl
[82] , : Unitary representations with non-zero cohomology, Comp. Math. 53 (1984), 51-90. | MR | Zbl | EuDML | Numdam
[83] : Représentations cristallines de torsion, Comp. Math. 108, (1997) 185-240. | MR | Zbl | DOI
[84] : Cohomologie des espaces de formes automorphes, d'après J. Franke, Séminaire Bourbaki, Exp. 809, Astérisque 241, 1997. | MR | Zbl | Numdam
[85] : On the constant term of a square integrable automorphic form, in Proc. Conf on Operator Algebras and Group Representations, held in Neptun (Romania), Eds. Arsene, Stratila, Verona, Voiculescu; Monographs and Studies in Mathematics, Pitman Publ., London 1984. | MR | Zbl
[86] : An application of the hard Lefschetz theorem, preprint 1996.
[87] : Four dimensional Galois representations, preprint, 1996.
[88] : On -adic representations for totally real fields, Ann. Math. 123, (1986), 407-456. | MR | Zbl | DOI
[89] : On -adic representations associated to modular forms, Inv. Math. 94, (1988), 529-573. | MR | Zbl | EuDML | DOI
[90] : Siegel's modular forms and the arithmetic of quadratic forms, Inv. Math. 60, (1980) 193-248. | MR | Zbl | EuDML | DOI
[91] : Letter to the authors, August 3, 1999.







