L 2 -cohomology and intersection homology of locally symmetric varieties, III
Théorie de Hodge - Luminy, Juin 1987, Astérisque, no. 179-180 (1989), pp. 245-278.
@incollection{AST_1989__179-180__245_0,
     author = {Zucker, Steven},
     title = {$L^2$-cohomology and intersection homology of locally symmetric varieties, {III}},
     booktitle = {Th\'eorie de Hodge - Luminy, Juin 1987},
     editor = {Barlet D. and Esnault H. and Elzein F. and Verdier Jean-Louis and Viehweg E.},
     series = {Ast\'erisque},
     pages = {245--278},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {179-180},
     year = {1989},
     zbl = {0705.14021},
     language = {en},
     url = {http://www.numdam.org/item/AST_1989__179-180__245_0/}
}
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Zucker, Steven. $L^2$-cohomology and intersection homology of locally symmetric varieties, III, dans Théorie de Hodge - Luminy, Juin 1987, Astérisque, no. 179-180 (1989), pp. 245-278. http://www.numdam.org/item/AST_1989__179-180__245_0/

[1] Ash, A., Mumford, D., Rapoport, M., Tai, Y. : Smooth Compactifications of Locally Symmetric Varieties. Mathematical Science Press, Brookline, MA, 1975. | Zbl

[2] Baily, W.: Satake's compactification of Vn * Amer. J. Math. 80 (1958), 348-364. | DOI | Zbl

[3] Baily, W., Borel, A.: Compactifications of arithmetic quotients of bounded symmetric domains. Ann. of Math. 84 (1966), 442-528. | DOI | Zbl

[4] Beilinson, A., Bernstein, J., Deligne, P.: Faisceaux pervers. Astérisque 100 (1982). | Numdam | Zbl

[5] Borel, A.: Stable real cohomology of arithmetic groups. Ann. Sci. ENS 7 (1974), 235-272. | EuDML | Numdam | Zbl

[6] Borel, A.: Regularization theorems in Lie algebra cohomology. Applications. Duke Math. J. 50 (1983), 605-624. | DOI | Zbl

[7] Borel, A.: L 2 -cohomology and intersection cohomology of certain arithmetic varieties. In: Emmy Noether in Bryn Mawr, Springer, 1983, 119-131. | DOI | Zbl

[8] Borel, A.: A vanishing theorem in relative Lie algebra cohomology. In: Algebraic Groups: Utrecht, 1986, Lecture Notes in Math. 1271, Springer, 1987. | Zbl

[9] Borel, A., et al.: Intersection Cohomology. Birkhäuser, Boston, 1984. | DOI | Zbl

[10] Borel, A., Casselman, W.: L 2 -cohomology of locally symmetric manifolds of finite volume. Duke Math. J. 50 (1983), 625-647. | DOI | Zbl

[11] Borel, A., Casselman, W.: Cohomologie d'intersection et L 2 -cohomologie de variétés arithmétiques de rang rationnel 2. CR Acad. Sc. Paris 301 (1985), 369-373. | Zbl

[12] Borel, A., Garland, H.: Laplacian and discrete spectrum of an arithmetic group. Amer. J. Math. 105 (1983), 309-335. | DOI | Zbl

[13] Borel, A., Wallach, N. : Continuous Cohomology, Discrete Subgroups and Representations of Reductive Groups. Annals of Math. Studies 94, Princeton Univ. Press, 1980. | Zbl

[14] Brylinski, J.-L., Labesse, J.-P.: Cohomologie d'intersection et fonctions L de certaines variétés de Shimura. Ann. Sci. ENS 17 (1984), 361-412. | EuDML | Numdam | Zbl

[15] Casselman, W.: L 2 -cohomology for groups of real rank one. In: Representation Theory of Reductive Groups, Birkhäuser, 1983, 69-84. | Zbl

[16] Casselman, W.: Introduction to the L 2 -cohomology of arithmetic quotients of bounded symmetric domains. In: Complex Analytic Singularities, Adv. Stud. Pure Math. 8 (1986), 69-93. | Zbl

[17] Cattani, E., Kaplan, A., Schmid, W.: L 2 and intersection cohomologies for a polarizable variation of Hodge structure. Inventiones Math. 87 (1987), 217-252. | DOI | EuDML | Zbl

[18] Cheeger, J.: On the Hodge theory of Riemannian pseudomanifolds. AMS Proc. Symposia Pure Math. 36 (1980), 91-146. | DOI | Zbl

[19] Cheeger, J., Goresky, M., Macpherson, R.: L 2 -cohomology and intersection homology of singular varieties. In: Seminar on Differential Geometry, Annals of Math. Studies 102 (1982), 303-340. | Zbl

[20] Gaffney, M.: Hilbert space methods in the theory of harmonic integrals. Transactions AMS 78 (1955), 426-444. | DOI | MR | Zbl

[21] Goresky, M., and Macpherson, R.: Intersection homology, II. Inventiones Math. 72 (1983), 77-129. | DOI | EuDML | MR | Zbl

[22] Harder, G.: On the cohomology of discrete arithmetically defined subgroups. In: Proceedings of the International Colloquium on Discrete Subgroups of Lie Groups and Applications, Oxford Univ. Press, 1975, 129-160. | MR | Zbl

[23] Helgason, S.: Differential Geometry, Lie Groups, and Symmetric Spaces. Academic Press, New York-San Francisco-London. 1978. | MR | Zbl

[24] Hörmander, L.: L 2 estimates and existence theorems for the ¯ operator. Acta Math. 113 (1965), 89-152. | DOI | MR | Zbl

[25] Kashiwara, M., Kawai, T.: The Poincaré lemma for variations of polarized Hodge structure. Publ. RIMS 23 (1987), 345-407. | DOI | MR | Zbl

[26] Kohn, J.: Harmonic integrals on strongly pseudo-convex manifolds, I. Ann. of Math. 78 (1963), 112-148. | DOI | MR | Zbl

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

[28] Looijenga, E.: L 2 -cohomology of locally symmetric varieties. Compositio Math. 67 (1988), 3-20. | EuDML | Numdam | MR | Zbl

[29] Matsushima, Y., and Murakami, S.: On vector bundle valued harmonic forms and automorphic forms on symmetric Riemannian manifolds. Ann. of Math. 78 (1963), 365-416. | DOI | MR | Zbl

[30] Matsushima, Y., and Murakami, S.: On certain cohomology groups attached to Hermitian symmetric spaces. Osaka J. Math. 2 (1965), 1-35. | MR | Zbl

[31] Raghunathan, M.: On the first cohomology of discrete subgroups of semi-simple Lie groups. Amer. J. Math. 87 (1965), 103-139. | DOI | MR | Zbl

[32] Raghunathan, M.: Vanishing theorems for cohomology groups associated to discrete subgroups of semi-simple Lie groups. Osaka J. Math. 3 (1966), 243-256. | MR | Zbl

Raghunathan, M.: Vanishing theorems for cohomology groups associated to discrete subgroups of semi-simple Lie groups. Osaka J. Math. 16 (1979), 295-299. | MR | Zbl

[33] Saito, Morihiko: Modules de Hodge polarisables. Preprint RIMS - 553, 1986. | MR | Zbl

[34] Saito, Morihiko: Mixed Hodge modules. Preprint RIMS - 585, 1987. | MR

Saito, Morihiko: Mixed Hodge modules.Proc. Japan Acad. 62 (1986), Ser. A., 360-363. | DOI | MR | Zbl

[35] Saper, L., Stern, M.: L 2 cohomology of arithmetic varieties. Proc. Natl. Acad. Sci. USA 84 (1987), 5516-5519. | DOI | MR | Zbl

[36] Saper, L., Stern, M.: L 2 -cohomology of arithmetic varieties. Ann. of Math. (to appear). | MR | Zbl

[37] Satake, I.: On the compactification of the Siegel space. J. Indian Math. Soc. 20 (1956), 259-281. | MR | Zbl

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

[39] Séminaire H. Cartan, Fonctions Automorphes, ENS 1957/58, vol. 2.

[40] Vogan, D., Zuckerman, G.: Unitary representations with non-zero cohomology. Compositio Math. 53 (1984), 51-90. | EuDML | Numdam | MR | Zbl

[41] Warner, G.: Harmonic Analysis on Semi-Simple Groups I. Springer-Verlag, Berlin-Heidelberg-New York, 1972. | MR | Zbl

[42] Zucker, S.: Locally homogeneous variations of Hodge structure. L'Enseignement Math. 27 (1981), 243-276. | MR | Zbl

[43] Zucker, S.: L 2 -cohomology of warped products and arithmetic groups. Inventiones Math. 70 (1982), 169-218. | DOI | EuDML | MR | Zbl

[44] Zucker, S.: L 2 -cohomology and intersection homology of locally symmetric varieties. AMS Proc. Symposia Pure Math. 40, Part 2 (1983), 675-680. | DOI | MR | Zbl

[45] Zucker, S.: On a theorem of Chern. Math. Zeit. 182 (1983), 87-94. | DOI | EuDML | MR | Zbl

[46] Zucker, S.: Satake compactifications. Commentarii Math. Helv. 58 (1983), 312-343. | DOI | EuDML | MR | Zbl

[47] Zucker, S.: L 2 -cohomology and intersection homology of locally symmetric varieties, II. Compositio Math. 59 (1986), 339-398. | EuDML | Numdam | MR | Zbl

[48] Zucker, S.: The Hodge structures on the intersection homology of varieties with isolated singularities. Duke Math. J. 55 (1987), 603-616. | DOI | MR | Zbl