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Inventiones mathematicae

, Volume 116, Issue 1, pp 139–213 | Cite as

Weighted cohomology

  • M. Goresky
  • G. Harder
  • R. MacPherson
Article

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References

  1. [A] Arthur, J.: TheL 2 Lefschetz numbers of Hecke operators. Invent. Math.97, 257–290(1989)Google Scholar
  2. [BS] Borel, A., Serre, J.-P.: Corners and arithmetic groups. Comm. Math. Helv.48, 436–491(1973)Google Scholar
  3. [AMRT] Ash, A., Mumford, D., Rapoport, M., Tai, Y.: Smooth compactifications of locally symmetric varieties. Math. Sci. Press, Brookline MA 1975Google Scholar
  4. [BB] Bailey, W., Borel, A.: Compactifications of arithmetic quotients of bounded symmetric domains. Ann. Math.84, 442–528 (1966)Google Scholar
  5. [B1] Borel, A.: Introduction aux groupes arithmétiques. Hermann, Paris 1968Google Scholar
  6. [B2] Borel, A.: Linear algebraic groups. (Graduate texts in mathematics vol.126.) Springer, New York Berlin Heidelberg 1991Google Scholar
  7. [B3] Borel, A.:L 2 cohomology and intersection cohomology of certain arithmetic varieties. (In: Emmy Noether at Bryn Mawr.) Springer, New York Berlin Heidelberg 1983Google Scholar
  8. [B4] Borel, A.: Regularization theorems in Lie algebra cohomology. Applications. Duke Math J.50, 605–623 (1983)Google Scholar
  9. [B-] Borel, A. et al.: Intersection cohomology. Birkhauser Boston, Boston 1984Google Scholar
  10. [BM] Borel, A., Moore, J. C.: Homology theory for locally compact spaces. Michigan Math. J7, 137–159(1960)Google Scholar
  11. [BW] Borel, A., Wallach, N.: Continuous cohomology, discrete subgroups and representations of reductive groups. Princeton University Press, Princeton NJ 1980Google Scholar
  12. [BT] Bott, R., Tu, L.: Differential forms in algebraic topology. (Graduate Texts in Mathematics vol82.) Springer, New York Berlin Heidelberg 1982Google Scholar
  13. [CE] Cartan, H., Eilsenberg, S.: Homological algebra. Princeton University Press, Princeton NJ 1956Google Scholar
  14. [E] van Est, W. T.: A generalization of the Cartan-Leray sequence, I, II. Indag. MathXX, 399–413(1958)Google Scholar
  15. [F] Franke, J.: WeightedL 2 cohomology. (To appear)Google Scholar
  16. [Go] Godement, R.: Topologie algébrique et théorie des faisceaux. Hermann, Paris 1958Google Scholar
  17. [GM1] Goresky, M., MacPherson, R.: Intersection homology theory. Topology19, 135–162(1980)Google Scholar
  18. [GM2] Goresky, M., MacPherson, R.: Intersection homology II. Invent. Math.72, 77–129(1983)Google Scholar
  19. [GM3] Goresky, M., MacPherson, R.: Lefschetz numbers of Hecke correspondences. In: Langlands R., Ramakrishnan D. (eds.) The zeta function of Picard modular surfaces. Centre de Recherches Mathématiques, Univ. de Montreal, Montreal 1992Google Scholar
  20. [GM4] Goresky, M., MacPherson, R.: Local contribution to the Lefschetz fixed point formula. Invent. Math.111, 1–33(1993)Google Scholar
  21. [GM5] Goresky, M., MacPherson, R.: Stratified Morse theory. (Ergebnisse Math. vol14.) Springer, Berlin Heidelberg New York 1989Google Scholar
  22. [GM6] Goresky, M., MacPherson, R.: Topological trace formula. (To appear)Google Scholar
  23. [H1] Harder, G.: A Gauss-Bonnet formula for discrete arithmetically defined groups. Ann. Sci. Ecole Norm. Sup.4, 409–455 (1971)Google Scholar
  24. [H2] Harder, G.: On the cohomology of discrete arithmetically defined groups. (In: Discrete subgroups of Lie groups, Proc. of Int. Coll., 1973.) Oxford University Press, Bombay, 1975. pp. 129–160Google Scholar
  25. [K] Kostant, B.: Lie algebra cohomology and the generalized Borel-Weil theorem. Ann. Math.74, 329–387(1961)Google Scholar
  26. [Kz] Koszul, J. L.: Homologie et cohomologie des algebres de Lie. Bull. Soc. Math. France78, 65–127(1950)Google Scholar
  27. [L] Looijenga, E.:L 2 cohomology of locally symmetric varieties. Comp. Math.67, 3–20(1988)Google Scholar
  28. [LR] Looijenga, E., Rapoport, R.: Weights in the cohomology of a Baily-Borel compactification. Proc. Symp. Pure Math53, 223–260Google Scholar
  29. [MM] MacPherson, R., McConnell, M.: Classical projective geometry and modular varieties. In: Igusa J.J. (ed.) Algebraic analysis, geometry, and number theory. Proc. of J.A.M.I. Inaugural Conference. Johns Hopkins University Press, Baltimore MD 1989Google Scholar
  30. [N] Nomizu, K.: On the cohomology of compact homogeneous spaces of nilpotent Lie groups. Ann. Math.59, 531–538(1954)Google Scholar
  31. [P] Pink, R.:Onl-adic sheaves on Shimura varieties and their higher direct images in the Baily-Borel compactification. Math. Ann. (To appear)Google Scholar
  32. [R1] Rapoport, M.: On the shape of the contribution of a fixed point on the boundary: the case of Q-rank one. In: Langlands R., Ramakrishnan D. (eds.) The zeta function of Picard modular surfaces. Centre de Recherches Mathématiques, Univ. de Montreal, Montreal 1992Google Scholar
  33. [R2] Rapoport, M.: (To appear)Google Scholar
  34. [SS] Saper, L., Stern, M.:L 2-cohomology of arithmetic varieties. Ann. Math.132, 1–69(1990)Google Scholar
  35. [Sp] Springer, T. A.: Linear algebraic groups. (Progress in Mathematics vol.9). Birkhauser Boston, Boston MA 1981Google Scholar
  36. [St] Stern, M.: Lefschetz formula for arithmetic varieties. Preliminary notes, Institute for Advanced Study, Princeton 1988Google Scholar
  37. [Ve] Verdier, J. L.: Dualité dans la cohomologie des espaces localement compactes. Sem. Bourbaki300, 1965Google Scholar
  38. [V] Vogan, D.: Representations of real reductive Lie groups. (Progress in Mathematics vol.15) Birkhauser Boston, Boston MA 1981Google Scholar
  39. [Z1] Zucker, S.:L 2 cohomology of warped products and arithmetic groups. Invent. Math.70, 169–218(1982)Google Scholar
  40. [Z2] Zucker, S.: Satake compactifications. Comm. Math. Helv.58, 312–343(1983)Google Scholar
  41. [Z3] Zucker, S.:L 2 cohomology and intersection homology of locally symmetric varieties II. Comp. Math.59, 339–398(1986)Google Scholar

Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • M. Goresky
    • 1
  • G. Harder
    • 2
  • R. MacPherson
    • 3
  1. 1.Department of MathematicsNortheastern UniversityBostonUSA
  2. 2.Mathematisches InstitutUniversität BonnBonnGermany
  3. 3.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA

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