Boundary cohomology of Shimura varieties. I. Coherent cohomology on toroidal compactifications
Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 27 (1994) no. 3, pp. 249-344.
@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},
     pages = {249--344},
     publisher = {Elsevier},
     volume = {Ser. 4, 27},
     number = {3},
     year = {1994},
     doi = {10.24033/asens.1695},
     mrnumber = {95a:14024},
     zbl = {0860.11030},
     language = {en},
     url = {http://archive.numdam.org/articles/10.24033/asens.1695/}
}
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Harris, Michael; Zucker, Steven. Boundary cohomology of Shimura varieties. I. Coherent cohomology on toroidal compactifications. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 27 (1994) no. 3, pp. 249-344. doi : 10.24033/asens.1695. http://archive.numdam.org/articles/10.24033/asens.1695/

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

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

[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 | Zbl

[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 | Zbl

[B1] A. Borel, Introduction aux groupes arithmétiques Hermann, Paris, 1969. | MR | Zbl

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

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

[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 | Zbl

[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 | Zbl

[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). | EuDML | MR | Zbl

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

[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 | Zbl

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

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

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

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

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

[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). | EuDML | MR | Zbl

[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 | Zbl

[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). | EuDML | Numdam | Zbl

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

[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 | Zbl

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

[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 | Zbl

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

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

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

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

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

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

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

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

[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 | Zbl

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

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

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

[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 | Zbl

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

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

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

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

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

[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). | EuDML | MR | Zbl

[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 | Zbl

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

[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). | EuDML | Zbl

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

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