Restriction of the holomorphic cohomology of a Shimura variety to a smaller Shimura variety

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Restriction of the holomorphic cohomology of a Shimura variety to a smaller Shimura variety

L. Clozel and T. N. Venkataramana

Source: Duke Math. J. Volume 95, Number 1 (1998), 51-106.

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Primary Subjects: 11G18

Secondary Subjects: 11F46, 11F55, 14G35, 22E55

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Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077229504
Mathematical Reviews number (MathSciNet): MR1646542
Zentralblatt MATH identifier: 01425159
Digital Object Identifier: doi:10.1215/S0012-7094-98-09502-3

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References

[An] G. Anderson, Theta functions and holomorphic differential forms on compact quotients of bounded symmetric domains, Duke Math. J. 50 (1983), no. 4, 1137–1170.

Mathematical Reviews (MathSciNet): MR85i:32047

Zentralblatt MATH: 0557.32006

Digital Object Identifier: doi:10.1215/S0012-7094-83-05049-4

Project Euclid: euclid.dmj/1077303494

[A] J. Arthur, Unipotent automorphic representations: Conjectures, Astérisque 171-172 (1989), 13–71, Orbites Unipotentes et Représentations, II, Soc. Math. France, Montrouge.

Mathematical Reviews (MathSciNet): MR91f:22030

Zentralblatt MATH: 0728.22014

[BBD] A. Beilinson, J. Bernstein, and P. Deligne, Faisceaux pervers, Analysis and Topology on Singular Spaces, I (Luminy, 1981), Astérisque, vol. 100, Soc. Math. France, Paris, 1982, pp. 5–171.

Mathematical Reviews (MathSciNet): MR86g:32015

Zentralblatt MATH: 0536.14011

[BR] D. Blasius and J. Rogawski, Zeta functions of Shimura varieties, Motives (Seattle, Wash., 1991), Proc. Sympos. Pure Math., Part 2, vol. 55, Amer. Math. Soc., Providence, 1994, pp. 525–571.

Mathematical Reviews (MathSciNet): MR95e:11051

Zentralblatt MATH: 0827.11033

[Bo1] A. Borel, Regularization theorems in Lie algebra cohomology: Applications, Duke Math. J. 50 (1983), no. 3, 605–623.

Mathematical Reviews (MathSciNet): MR84h:17009

Zentralblatt MATH: 0528.22010

Digital Object Identifier: doi:10.1215/S0012-7094-83-05028-7

Project Euclid: euclid.dmj/1077303325

[Bo2] A. Borel, Works, Springer-Verlag, Berlin, 1983.

[Bo3] A. Borel, Linear Algebraic Groups, 2d ed., Grad. Texts in Math., vol. 126, Springer-Verlag, New York, 1991.

Mathematical Reviews (MathSciNet): MR92d:20001

Zentralblatt MATH: 0726.20030

[BoJ] A. Borel and H. Jacquet, Automorphic forms and automorphic representations, Automorphic Forms, Representations and $L$-Functions (Oregon State Univ., Corvallis, Ore., 1977), Part 1, Proc. Sympos. Pure Math., vol. 33, Amer. Math. Soc., Providence, 1979, pp. 189–207.

Mathematical Reviews (MathSciNet): MR81m:10055

Zentralblatt MATH: 0414.22020

[BoW] A. Borel and N. Wallach, Continuous Cohomology, Discrete Subgroups, and Representations of Reductive Groups, Ann. of Math. Stud., vol. 94, Princeton Univ. Press, Princeton; Univ. of Tokyo Press, Tokyo, 1980.

Mathematical Reviews (MathSciNet): MR83c:22018

Zentralblatt MATH: 0443.22010

[Bor] M. V. Borovoi, The action of the Galois group on the rational cohomology classes of type $(p,\,p)$ of abelian varieties, Mat. Sb. (N.S.) 94(136) (1974), 649–652, 656.

Mathematical Reviews (MathSciNet): MR50:4588

Zentralblatt MATH: 0326.14013

[C1] L. Clozel, Motifs et formes automorphes: Applications du principe de fonctorialité, Automorphic Forms, Shimura Varieties and $L$-Functions, I (Ann Arbor, Mich., 1988), Perspect. Math., vol. 10, Academic Press, Boston, 1990, pp. 77–159.

Mathematical Reviews (MathSciNet): MR91k:11042

Zentralblatt MATH: 0705.11029

[C2] L. Clozel, Produits dans la cohomologie holomorphe des variétés de Shimura, J. Reine Angew. Math. 430 (1992), 69–83.

Mathematical Reviews (MathSciNet): MR93i:14017

Zentralblatt MATH: 0787.14011

Digital Object Identifier: doi:10.1515/crll.1992.430.69

[C3] L. Clozel, Produits dans la cohomologie holomorphe des variétés de Shimura. II. Calculs et applications, J. Reine Angew. Math. 444 (1993), 1–15.

Mathematical Reviews (MathSciNet): MR95b:22030

Zentralblatt MATH: 0781.14014

Digital Object Identifier: doi:10.1515/crll.1993.444.1

[C4] L. Clozel, On the cohomology of Kottwitz's arithmetic varieties, Duke Math. J. 72 (1993), no. 3, 757–795.

Mathematical Reviews (MathSciNet): MR95b:11055

Zentralblatt MATH: 0974.11019

Digital Object Identifier: doi:10.1215/S0012-7094-93-07229-8

Project Euclid: euclid.dmj/1077289630

[D1] P. Deligne, Travaux de Shimura, Séminaire Bourbaki, 23ème année (1970/71), Exp. No. 389, Springer, Berlin, 1971, 123–165. Lecture Notes in Math., Vol. 244.

Mathematical Reviews (MathSciNet): MR58:16675

Zentralblatt MATH: 0225.14007

[D2] P. Deligne, Théorie de Hodge, II, Inst. Hautes Études Sci. Publ. Math. (1971), no. 40, 5–57.

Mathematical Reviews (MathSciNet): MR58:16653a

Zentralblatt MATH: 0219.14007

Digital Object Identifier: doi:10.1007/BF02684692

[D3] P. Deligne, Théorie de Hodge, III, Inst. Hautes Études Sci. Publ. Math. (1974), no. 44, 5–77.

Mathematical Reviews (MathSciNet): MR58:16653b

Zentralblatt MATH: 0237.14003

Digital Object Identifier: doi:10.1007/BF02685881

[D4] P. Deligne, Variétés de Shimura: Interprétation modulaire et techniques de construction de modèles canoniques, Automorphic Forms, Representations and $L$-Functions (Oregon State Univ., Corvallis, Ore., 1977), Part 2, Proc. Sympos. Pure Math., vol. 33, Amer. Math. Soc., Providence, 1979, pp. 247–289.

Mathematical Reviews (MathSciNet): MR81i:10032

Zentralblatt MATH: 0437.14012

[DMOS] P. Deligne, J. S. Milne, A. Ogus, and K.-Y. Shih, Hodge Cycles, Motives, and Shimura Varieties, Lecture Notes in Math., vol. 900, Springer-Verlag, Berlin, 1982.

Mathematical Reviews (MathSciNet): MR84m:14046

Zentralblatt MATH: 0465.00010

[FP] E. Freitag and K. Pommerening, Reguläre Differentialformen des Körpers der Siegelschen Modulfunktionen, J. Reine Angew. Math. 331 (1982), 207–220.

Mathematical Reviews (MathSciNet): MR84a:10026

Zentralblatt MATH: 0506.10025

[GM] M. Goresky and R. MacPherson, Intersection homology, II, Invent. Math. 72 (1983), no. 1, 77–129.

Mathematical Reviews (MathSciNet): MR84i:57012

Zentralblatt MATH: 0529.55007

Digital Object Identifier: doi:10.1007/BF01389130

[Ha1] G. Harder, Eisenstein cohomology of arithmetic groups. The case $\rm GL\sb 2$, Invent. Math. 89 (1987), no. 1, 37–118.

Mathematical Reviews (MathSciNet): MR89b:22018

Zentralblatt MATH: 0629.10023

Digital Object Identifier: doi:10.1007/BF01404673

[Ha2] G. Harder, Kohomologie des Arithmetische Gruppen, in preparation.

[HC] Harish-Chandra, Automorphic Forms on Semi-simple Lie Groups, Lecture Notes in Math., vol. 62, Springer-Verlag, Berlin, 1968.

Mathematical Reviews (MathSciNet): MR38:1216

Zentralblatt MATH: 0186.04702

[H1] M. Harris, Functorial properties of toroidal compactifications of locally symmetric varieties, Proc. London Math. Soc. (3) 59 (1989), no. 1, 1–22.

Mathematical Reviews (MathSciNet): MR90h:11048

Zentralblatt MATH: 0711.14011

Digital Object Identifier: doi:10.1112/plms/s3-59.1.1

[H2] M. Harris, Automorphic forms of $\overline\partial$-cohomology type as coherent cohomology classes, J. Differential Geom. 32 (1990), no. 1, 1–63.

Mathematical Reviews (MathSciNet): MR91g:11064

Zentralblatt MATH: 0711.14012

Project Euclid: euclid.jdg/1214445036

[KMR] V. Kumar Murty and D. Ramakrishnan, The Albanese of unitary Shimura varieties, The Zeta Functions of Picard Modular Surfaces, Univ. Montréal, Montréal, 1992, pp. 445–464.

Mathematical Reviews (MathSciNet): MR93b:14039

Zentralblatt MATH: 0828.14013

[Ku] S. Kumaresan, On the canonical $k$-types in the irreducible unitary $g$-modules with nonzero relative cohomology, Invent. Math. 59 (1980), no. 1, 1–11.

Mathematical Reviews (MathSciNet): MR83c:17011

Zentralblatt MATH: 0442.22010

Digital Object Identifier: doi:10.1007/BF01390311

[Lo] E. Looijenga, $L^2$-cohomology of locally symmetric varieties, Compositio Math. 67 (1988), no. 1, 3–20.

Mathematical Reviews (MathSciNet): MR90a:32044

Zentralblatt MATH: 0658.14010

[MW] C. Moeglin and J.-L. Waldspurger, Décomposition spectrale et séries d'Eisenstein, Progress in Mathematics, vol. 113, Birkhäuser Verlag, Basel, 1994.

Mathematical Reviews (MathSciNet): MR95d:11067

Zentralblatt MATH: 0794.11022

[Oda] T. Oda, A note on the Albanese variety of an arithmetic quotient of the complex hyperball, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 28 (1981), no. 3, 481–486.

Mathematical Reviews (MathSciNet): MR83j:14035

Zentralblatt MATH: 0528.14022

[P1] R. Parthasarathy, Criteria for the unitarizability of some highest weight modules, Proc. Indian Acad. Sci. Sect. A Math. Sci. 89 (1980), no. 1, 1–24.

Mathematical Reviews (MathSciNet): MR82c:22020

Zentralblatt MATH: 0434.22011

Digital Object Identifier: doi:10.1007/BF02881021

[P2] R. Parthasarathy, Holomorphic forms in $\Gamma \backslash G/K$ and Chern classes, Topology 21 (1982), no. 2, 157–178.

Mathematical Reviews (MathSciNet): MR83b:32029

Zentralblatt MATH: 0484.57026

Digital Object Identifier: doi:10.1016/0040-9383(82)90003-9

[PS] I. I. Piatetski-Shapiro, Interrelations between the Tate and Hodge hypotheses for abelian varieties, Mat. Sb. (N.S.) 85(127) (1971), 610–620.

Mathematical Reviews (MathSciNet): MR45:3422

Zentralblatt MATH: 0229.14014

[SS] L. Saper and M. Stern, $L_2$-cohomology of arithmetic varieties, Ann. of Math. (2) 132 (1990), no. 1, 1–69.

Mathematical Reviews (MathSciNet): MR91m:14027

Zentralblatt MATH: 0722.14009

Digital Object Identifier: doi:10.2307/1971500

[Se1] J.-P. Serre, Abelian $l$-adic Representations and Elliptic Curves, McGill University lecture notes written with the collaboration of Willem Kuyk and John Labute, Benjamin, New York, 1968.

Mathematical Reviews (MathSciNet): MR41:8422

Zentralblatt MATH: 0186.25701

[Se2] J.-P. Serre, Représentations $l$-adiques, Algebraic Number Theory, Kyoto International Symposium, Res. Inst. Math. Sci., Univ. Kyoto, Kyoto, 1976, Japan Soc. Promotion Sci., Tokyo, 1977, pp. 177–193.

Mathematical Reviews (MathSciNet): MR57:16310

Zentralblatt MATH: 0406.14015

[Sh] G. Shimura, Automorphic forms and the periods of abelian varieties, J. Math. Soc. Japan 31 (1979), no. 3, 561–592.

Mathematical Reviews (MathSciNet): MR81j:10034

Zentralblatt MATH: 0456.10015

Digital Object Identifier: doi:10.2969/jmsj/03130561

Project Euclid: euclid.jmsj/1240319184

[ST] G. Shimura and Y. Taniyama, Complex Multiplication of Abelian Varieties and Its Applications to Number Theory, Publ. Math. Soc. Japan, vol. 6, Math. Soc. Japan, Tokyo, 1961.

Mathematical Reviews (MathSciNet): MR23:A2419

Zentralblatt MATH: 0112.03502

[T] J. Tate, Number theoretic background, Automorphic Forms, Representations and $L$-Functions (Oregon State Univ., Corvallis, Ore, 1977), Part 2, Proc. Sympos. Pure Math., vol. 33, Amer. Math. Soc., Providence, 1979, pp. 3–26.

Mathematical Reviews (MathSciNet): MR80m:12009

Zentralblatt MATH: 0422.12007

[VZ] D. Vogan, Jr. and G. Zuckerman, Unitary representations with nonzero cohomology, Compositio Math. 53 (1984), no. 1, 51–90.

Mathematical Reviews (MathSciNet): MR86k:22040

Zentralblatt MATH: 0692.22008

[W] A. Weil, On the theory of complex multiplication, Proceedings of the International Symposium on Algebraic Number Theory, Tokyo and Nikko, 1955, Science Council of Japan, Tokyo, 1956, pp. 9–22.

Mathematical Reviews (MathSciNet): MR18,673a

Zentralblatt MATH: 0074.26802

[Weis] R. Weissauer, Differentialformen zu Untergruppen der Siegelschen Modulgruppe zweiten Grades, J. Reine Angew. Math. 391 (1988), 100–156.

Mathematical Reviews (MathSciNet): MR89i:32074

Zentralblatt MATH: 0657.10022

Digital Object Identifier: doi:10.1515/crll.1988.391.100

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