Boundary cohomology of Shimura varieties. I. Coherent cohomology on toroidal compactifications

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1. [A] J. ARTHUR, Eisenstein series and the trace formula (Proc. Symp. Pure Math., part 1, Vol. XXXIII, 1979, pp. 253-274). Zbl0431.22016MR81b:10020
2. [AMRT] A. ASH, D. MUMFORD, M. RAPOPORT and Y.-S. TAI, Smooth Compactification of Locally Symmetric Varieties (Math. Sci. Press, Brookline, Mass., 1975). Zbl0334.14007MR56 #15642
3. [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). Zbl0154.08602MR35 #6870
4. [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). Zbl0576.22015MR86i:22032
5. [B1] A. BOREL, Introduction aux groupes arithmétiques Hermann, Paris, 1969. Zbl0186.33202MR39 #5577
6. [B2] A. BOREL, Stable real cohomology of arithmetic groups (Ann. Scient. Ec. Norm. Sup., Vol. 7, 1974, pp. 235-272). Zbl0316.57026MR52 #8338
7. [BS] A. BOREL and J.-P. SERRE, Corners and arithmetic groups (Comm. Math. Helv., Vol. 48, 1973, pp. 436-491). Zbl0274.22011MR52 #8337
8. [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). Zbl0443.22010MR83c:22018
9. [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. 
10. [Br2] J.-L. BRYLINSKI, "1-motifs" et formes automorphes (Publ. Math. Univ. Paris VII, Vol. 15, 1983, pp. 43-106). Zbl0565.14001MR85g:11047
11. [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). Zbl0516.14005MR84a:32046
12. [D1] P. DELIGNE, Équations différentielles à points singuliers réguliers (Lect. Notes in Math., Vol. 163, 1970). Zbl0244.14004MR54 #5232
13. [D2] P. DELIGNE, Espaces hermitiens symétriques, notes from a course at I.H.E.S., 1973. 
14. [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). Zbl0437.14012MR81i:10032
15. [D4] P. DELIGNE, La Conjecture de Weil, II (Publ. Math. I.H.E.S., Vol. 52, 1980, pp. 137-252). Zbl0456.14014MR83c:14017
16. [D5] P. DELIGNE, Travaux de Shimura, Séminaire Bourbaki, 1970-1971, exp. 389 (Lecture Notes in Math., Vol. 244, 1972, pp. 123-165). Zbl0225.14007MR58 #16675
17. [D6] P. DELIGNE, Théorie de Hodge, III (Publ. Math. I.H.E.S., Vol. 44, 1974, pp. 5-77). Zbl0237.14003MR58 #16653b
18. [ES] S. EILENBERG and N. STEENROD, Foundations of Algebraic Topology, Princeton University Press, Princeton, 1952. Zbl0047.41402MR14,398b
19. [F] J. FRANKE, Harmonic analysis in weighted L2-spaces, Preprint 1991. 
20. [G] R. GODEMENT, Topologie Algébrique et Théorie des Faisceaux, Hermann, Paris, 1964. 
21. [Ha1] G. HARDER, Eisenstein cohomology of arithmetic groups : The case GL2 (Invent. Math., Vol. 89, 1987, pp. 37-118). Zbl0629.10023MR89b:22018
22. [Ha2] G. HARDER, Arithmetische Eigenschaften von Eisensteinklassen, die modulare Konstruktion von gemischten Motiven und von Erweiterungen endlicher Galoismoduln. Preprint 1989-1990. 
23. [H1] M. HARRIS, Eisenstein series on Shimura varieties (Ann. of Math., Vol. 119, 1984, pp. 59-94). Zbl0589.10030MR85j:11052
24. [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). Zbl0612.14019
25. [H3] M. HARRIS, Functorial properties of toroidal compactifications of locally symmetric varieties (Proc. Lon. Math. Soc., Vol. 59, 1989, pp. 1-22). Zbl0711.14011MR90h:11048
26. [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). Zbl0716.14011MR91g:11063
27. [H5] M. HARRIS, Automorphic forms of ∂-cohomology type as coherent cohomology classes (J. Diff. Geom., Vol. 32, 1990, pp. 1-63). Zbl0711.14012MR91g:11064
28. [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). Zbl0597.32025MR88a:32036
29. [He] S. HELGASON, Differential Geometry, Lie Groups, and Symmetric Spaces, Academic Press, New York, 1978. Zbl0451.53038MR80k:53081
30. [J] R. JOSHUA, Equivariant intersection cohomology-a survey (Invariant Theory, Contemp. Math., Vol. 88, 1989, pp. 25-31). Zbl0686.14016MR90f:55012
31. [Ka] M. KASHIWARA, The asymptotic behavior of a variation of Hodge structure (Publ. RIMS Kyoto Univ., Vol. 21, 1985, pp. 853-875). Zbl0594.14012MR87h:32049
32. [KKMS] G. KEMPF, F. KNUDSEN, D. MUMFORD and B. SAINT-DONAT, Toroidal embeddings (Lecture Notes in Math., Vol. 339, 1973). Zbl0271.14017MR49 #299
33. [K] B. KOSTANT, Lie algebra cohomology and the generalized Borel-Weil theorem (Ann. of Math., Vol. 74, 1961, pp. 329-387). Zbl0134.03501MR26 #265
34. [Ko] J.-L. KOSZUL, Sur certains groupes de transformations de Lie, Colloque de Géométrie Différentielle (Coll. CNRS, Vol. 71, 1953, pp. 137-141). Zbl0101.16201MR15,600g
35. [Kr] S. KRANTZ, Function Theory of Several Complex Variables, John Wiley, New York, 1982. Zbl0471.32008MR84c:32001
36. [L] E. LOOIJENGA, L2-cohomology of locally symmetric varieties (Compositio Math., Vol. 67, 1988, pp. 3-20). Zbl0658.14010MR90a:32044
37. [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). Zbl0704.14016MR91a:11027
38. [Mu1] D. MUMFORD, Abelian Varieties, Oxford University Press, Oxford, 1970. Zbl0223.14022MR44 #219
39. [Mu2] D. MUMFORD, Hirzebruch's proportionality theorem in the non-compact case (Invent. Math., Vol. 42, 1977, pp. 239-272). Zbl0365.14012MR81a:32026
40. [O] T. ODA, Convex Bodies in Algebraic Geometry : An Introduction to the Theory of Toric Varieties, Springer-Verlag, Berlin, 1988. Zbl0628.52002
41. [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). MR37 #4834
42. [P] R. PINK, Arithmetical compactification of mixed Shimura varieties (Bonn Dissertation, 1989). Zbl0748.14007
43. [S1] I. SATAKE, On compactifications of the quotient spaces for arithmetically defined discontinuous groups (Ann. of Math., Vol. 72, 1960, pp. 555-580). Zbl0146.04701MR30 #594
44. [S2] I. SATAKE, Algebraic Structures of Symmetric Domains, Iwanami Shoten and Princeton Univ. Press, 1980. Zbl0483.32017MR82i:32003
45. [Sc] W. SCHMID, Variation of Hodge structure : The singularities of the period mapping (Inventiones Math., Vol. 22, 1973, pp. 211-319). Zbl0278.14003MR52 #3157
46. [Sch] J. SCHWERMER, Kohomologie arithmetisch definierter Gruppen und Eisensteinreihen (Lecture Notes in Math., Vol. 988, 1983). Zbl0506.22015MR87i:22034
47. [Sj] R. SJAMAAR, "L2-cohomology of orbit spaces", Univ. of Utrecht. Preprint No. 525, 1988. 
48. [SZ] J. STEENBRINK, and S. ZUCKER, Variation of mixed Hodge structure, I (Inventiones Math., Vol. 80, 1985, pp. 489-542). Zbl0626.14007MR87h:32050a
49. [W] F. L. WILLIAMS, Discrete series multiplicities in L² (Γ) (II) : proof of Langlands’ conjecture (Amer. J. Math., Vol. 107, 1985, pp. 367-376). Zbl0569.22010MR86h:22025
50. [WK] J. WOLF and A. KORÁNYI, Generalized Cayley transformations of bounded symmetric domains (Amer. J. Math., Vol. 87, 1965, pp. 899-939). Zbl0137.27403MR33 #229
51. [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). Zbl0753.14017
52. [Z2] S. ZUCKER, L2-cohomology and intersection homology of locally symmetric varieties, II (Compositio Math., Vol. 59, 1986, pp. 339-398). Zbl0624.14014MR89i:32073