Boundary cohomology of Shimura varieties. I. Coherent cohomology on toroidal compactifications
Harris, Michael ; Zucker, Steven
Annales scientifiques de l'École Normale Supérieure, Tome 27 (1994), p. 249-344 / Harvested from Numdam
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@article{ASENS_1994_4_27_3_249_0,
     author = {Harris, Michael and Zucker, Steven},
     title = {Boundary cohomology of Shimura varieties. I. Coherent cohomology on toroidal compactifications},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     volume = {27},
     year = {1994},
     pages = {249-344},
     doi = {10.24033/asens.1695},
     mrnumber = {95a:14024},
     zbl = {0860.11030},
     language = {en},
     url = {http://dml.mathdoc.fr/item/ASENS_1994_4_27_3_249_0}
}

Harris, Michael; Zucker, Steven. Boundary cohomology of Shimura varieties. I. Coherent cohomology on toroidal compactifications. Annales scientifiques de l'École Normale Supérieure, Tome 27 (1994) pp. 249-344. doi : 10.24033/asens.1695. http://gdmltest.u-ga.fr/item/ASENS_1994_4_27_3_249_0/

[A] J. Arthur, Eisenstein series and the trace formula (Proc. Symp. Pure Math., part 1, Vol. XXXIII, 1979, pp. 253-274). | MR 546601 | MR 81b:10020 | Zbl 0431.22016

[AMRT] A. Ash, D. Mumford, M. Rapoport and Y.-S. Tai, Smooth Compactification of Locally Symmetric Varieties (Math. Sci. Press, Brookline, Mass., 1975). | MR 457437 | MR 56 #15642 | Zbl 0334.14007

[BB] W. L. Baily Jr. and A. Borel, Compactification of arithmetic quotients of bounded symmetric domains (Ann. of Math., Vol. 84, 1966, pp. 442-528). | MR 216035 | MR 35 #6870 | Zbl 0154.08602

[Bl] B. E. Blank, Knapp-Wallach Szegö integrals and generalized principal series representations : the parabolic rank one case (J. Fun. Analysis, Vol. 60, 1985, pp. 127-145). | MR 777234 | MR 86i:22032 | Zbl 0576.22015

[B1] A. Borel, Introduction aux groupes arithmétiques Hermann, Paris, 1969. | MR 244260 | MR 39 #5577 | Zbl 0186.33202

[B2] A. Borel, Stable real cohomology of arithmetic groups (Ann. Scient. Ec. Norm. Sup., Vol. 7, 1974, pp. 235-272). | Numdam | MR 387496 | MR 52 #8338 | Zbl 0316.57026

[BS] A. Borel and J.-P. Serre, Corners and arithmetic groups (Comm. Math. Helv., Vol. 48, 1973, pp. 436-491). | MR 387495 | MR 52 #8337 | Zbl 0274.22011

[BW] A. Borel and N. Wallach, Continuous Cohomology, Discrete Subgroups, and Representations of Reductive Groups Princeton, NJ. (Ann. of Math. Studies, Vol. 94, Princeton Univ. Press, 1980). | MR 554917 | MR 83c:22018 | Zbl 0443.22010

[Br1] J.-L. Brylinski, Algébricité du quotient par un groupe discret d'un domaine de Siegel de 3e espèce, provenant d'un espace hermitien symétrique, manuscrit, 1979.

[Br2] J.-L. Brylinski, "1-motifs" et formes automorphes (Publ. Math. Univ. Paris VII, Vol. 15, 1983, pp. 43-106). | MR 85g:11047 | Zbl 0565.14001

[CK] E. Cattani and A. Kaplan, Polarized mixed Hodge structure and the monodromy of a variation of Hodge structure (Inventiones Math., Vol. 67, 1982, pp. 101-115). | MR 664326 | MR 84a:32046 | Zbl 0516.14005

[D1] P. Deligne, Équations différentielles à points singuliers réguliers (Lect. Notes in Math., Vol. 163, 1970). | MR 417174 | MR 54 #5232 | Zbl 0244.14004

[D2] P. Deligne, Espaces hermitiens symétriques, notes from a course at I.H.E.S., 1973.

[D3] P. Deligne, Variétés de Shimura : Interprétation modulaire et techniques de construction de modèles canoniques (Proc. Symp. Pure Math., part 2, Vol. XXXIII, 1979, pp. 247-290). | MR 546620 | MR 81i:10032 | Zbl 0437.14012

[D4] P. Deligne, La Conjecture de Weil, II (Publ. Math. I.H.E.S., Vol. 52, 1980, pp. 137-252). | Numdam | MR 83c:14017 | Zbl 0456.14014

[D5] P. Deligne, Travaux de Shimura, Séminaire Bourbaki, 1970-1971, exp. 389 (Lecture Notes in Math., Vol. 244, 1972, pp. 123-165). | Numdam | MR 58 #16675 | Zbl 0225.14007

[D6] P. Deligne, Théorie de Hodge, III (Publ. Math. I.H.E.S., Vol. 44, 1974, pp. 5-77). | Numdam | MR 58 #16653b | Zbl 0237.14003

[ES] S. Eilenberg and N. Steenrod, Foundations of Algebraic Topology, Princeton University Press, Princeton, 1952. | MR 14,398b | Zbl 0047.41402

[F] J. Franke, Harmonic analysis in weighted L2-spaces, Preprint 1991. | Zbl 0938.11026

[G] R. Godement, Topologie Algébrique et Théorie des Faisceaux, Hermann, Paris, 1964.

[Ha1] G. Harder, Eisenstein cohomology of arithmetic groups : The case GL2 (Invent. Math., Vol. 89, 1987, pp. 37-118). | MR 89b:22018 | Zbl 0629.10023

[Ha2] G. Harder, Arithmetische Eigenschaften von Eisensteinklassen, die modulare Konstruktion von gemischten Motiven und von Erweiterungen endlicher Galoismoduln. Preprint 1989-1990.

[H1] M. Harris, Eisenstein series on Shimura varieties (Ann. of Math., Vol. 119, 1984, pp. 59-94). | MR 85j:11052 | Zbl 0589.10030

[H2] M. Harris, Arithmetic vector bundles and automorphic forms on Shimura varieties : I (Inventiones Math., Vol. 82, 1985, pp. 151-189) ; II (Compositio Math., Vol. 60, 1986, pp. 323-378). | Numdam | Zbl 0612.14019

[H3] M. Harris, Functorial properties of toroidal compactifications of locally symmetric varieties (Proc. Lon. Math. Soc., Vol. 59, 1989, pp. 1-22). | MR 90h:11048 | Zbl 0711.14011

[H4] M. Harris, Automorphic forms and the cohomology of vector bundles on Shimura Varieties (Proceedings of the Ann Arbor Conference on Shimura Varieties and Automorphic Forms, Progress in Mathematics, Academic Press, New York, Vol. II, 1989, pp. 41-92). | MR 91g:11063 | Zbl 0716.14011

[H5] M. Harris, Automorphic forms of ∂-cohomology type as coherent cohomology classes (J. Diff. Geom., Vol. 32, 1990, pp. 1-63). | MR 91g:11064 | Zbl 0711.14012

[HP] M. Harris and D. H. Phong, Cohomologie de Dolbeault à croissance logarithmique à l'infini (C. R. Acad. Sci. Paris, Vol. 302, 1986, pp. 307-310). | MR 88a:32036 | Zbl 0597.32025

[He] S. Helgason, Differential Geometry, Lie Groups, and Symmetric Spaces, Academic Press, New York, 1978. | MR 80k:53081 | Zbl 0451.53038

[J] R. Joshua, Equivariant intersection cohomology-a survey (Invariant Theory, Contemp. Math., Vol. 88, 1989, pp. 25-31). | MR 90f:55012 | Zbl 0686.14016

[Ka] M. Kashiwara, The asymptotic behavior of a variation of Hodge structure (Publ. RIMS Kyoto Univ., Vol. 21, 1985, pp. 853-875). | MR 87h:32049 | Zbl 0594.14012

[KKMS] G. Kempf, F. Knudsen, D. Mumford and B. Saint-Donat, Toroidal embeddings (Lecture Notes in Math., Vol. 339, 1973). | MR 49 #299 | Zbl 0271.14017

[K] B. Kostant, Lie algebra cohomology and the generalized Borel-Weil theorem (Ann. of Math., Vol. 74, 1961, pp. 329-387). | MR 26 #265 | Zbl 0134.03501

[Ko] J.-L. Koszul, Sur certains groupes de transformations de Lie, Colloque de Géométrie Différentielle (Coll. CNRS, Vol. 71, 1953, pp. 137-141). | MR 15,600g | Zbl 0101.16201

[Kr] S. Krantz, Function Theory of Several Complex Variables, John Wiley, New York, 1982. | MR 84c:32001 | Zbl 0471.32008

[L] E. Looijenga, L2-cohomology of locally symmetric varieties (Compositio Math., Vol. 67, 1988, pp. 3-20). | Numdam | MR 90a:32044 | Zbl 0658.14010

[Mi] J. S. Milne, Canonical models of (mixed) Shimura varieties and automorphic vector bundles (Proceedings of the Ann Arbor Conference on Shimura Varieties and Automorphic Forms, Progress in Mathematics, Academic Press, New York, Vol. I, 1989, pp. 283-414). | MR 91a:11027 | Zbl 0704.14016

[Mu1] D. Mumford, Abelian Varieties, Oxford University Press, Oxford, 1970. | MR 44 #219 | Zbl 0223.14022

[Mu2] D. Mumford, Hirzebruch's proportionality theorem in the non-compact case (Invent. Math., Vol. 42, 1977, pp. 239-272). | MR 81a:32026 | Zbl 0365.14012

[O] T. Oda, Convex Bodies in Algebraic Geometry : An Introduction to the Theory of Toric Varieties, Springer-Verlag, Berlin, 1988. | Zbl 0628.52002

[O-O] K. Okamoto and H. Ozeki, On square integrable d-bar cohomology of Hermitian symmetric spaces (Osaka J. Math., Vol. 4, 1967, pp. 85-94). | MR 37 #4834 | Zbl 0173.23702

[P] R. Pink, Arithmetical compactification of mixed Shimura varieties (Bonn Dissertation, 1989). | Zbl 0748.14007

[S1] I. Satake, On compactifications of the quotient spaces for arithmetically defined discontinuous groups (Ann. of Math., Vol. 72, 1960, pp. 555-580). | MR 30 #594 | Zbl 0146.04701

[S2] I. Satake, Algebraic Structures of Symmetric Domains, Iwanami Shoten and Princeton Univ. Press, 1980. | MR 82i:32003 | Zbl 0483.32017

[Sc] W. Schmid, Variation of Hodge structure : The singularities of the period mapping (Inventiones Math., Vol. 22, 1973, pp. 211-319). | MR 52 #3157 | Zbl 0278.14003

[Sch] J. Schwermer, Kohomologie arithmetisch definierter Gruppen und Eisensteinreihen (Lecture Notes in Math., Vol. 988, 1983). | MR 87i:22034 | Zbl 0506.22015

[Sj] R. Sjamaar, "L2-cohomology of orbit spaces", Univ. of Utrecht. Preprint No. 525, 1988.

[SZ] J. Steenbrink, and S. Zucker, Variation of mixed Hodge structure, I (Inventiones Math., Vol. 80, 1985, pp. 489-542). | MR 87h:32050a | Zbl 0626.14007

[W] F. L. Williams, Discrete series multiplicities in L² (Γ\G) (II) : proof of Langlands' conjecture (Amer. J. Math., Vol. 107, 1985, pp. 367-376). | MR 86h:22025 | Zbl 0569.22010

[WK] J. Wolf and A. Korányi, Generalized Cayley transformations of bounded symmetric domains (Amer. J. Math., Vol. 87, 1965, pp. 899-939). | MR 33 #229 | Zbl 0137.27403

[Z1] S. Zucker, Satake compactifications (Comm. Math. Helv., Vol. 58, 1983, pp. 312-343). Errata in : Lp-cohomology and Satake compactifications. In : J. NOGUCHI and T. OHSAWA, eds., Prospects in Complex Geometry, (Lecture Notes in Math., Vol. 1468, 1991, pp. 317-339). | Zbl 0753.14017

[Z2] S. Zucker, L2-cohomology and intersection homology of locally symmetric varieties, II (Compositio Math., Vol. 59, 1986, pp. 339-398). | Numdam | MR 89i:32073 | Zbl 0624.14014