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Formality of equivariant intersection cohomology of algebraic varieties

Author: Andrzej Weber
Journal: Proc. Amer. Math. Soc. 131 (2003), 2633-2638
MSC (2000): Primary 14F43, 55N25; Secondary 55N33
Published electronically: April 23, 2003
MathSciNet review: 1974316
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Abstract: We present a proof that the equivariant intersection cohomology of any complete algebraic variety acted by a connected algebraic group $G$ is a free module over $H^{*}(BG)$.

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  • [AB] Atiyah, M.F.; Bott, R., The moment map and equivariant cohomology, Topology 23 (1984), 1-28. MR 85e:58041
  • [AM] Adams, J. F.; Mahmud, Z., Maps between classifying spaces, Inv. Math. 35 (1976), 1-41. MR 54:11331
  • [BBD] Beilinson, A.A.; Bernstein, J.; Deligne, P., Faisceaux pervers, Asterisque 100 (1982). MR 86g:32015
  • [BL] Bernstein, J.; Lunts, V., Equivariant sheaves and functors, Lecture Notes in Mathematics, vol. 1578, Springer-Verlag, Berlin, 1994. MR 95k:55012
  • [B-B] Bia\lynicki-Birula A., On induced actions of algebraic groups, Ann. Inst. Fourier, Grenoble 43 (2) (1993), 365-368. MR 94c:14041
  • [Br] Brylinski, J-L., Equivariant intersection cohomology, Kazhdan-Lusztig theory and related topics. Proceedings of an AMS special session, held May 19-20, 1989 at the University of Chicago, Lake Shore Campus, Chicago, IL, USA. American Mathematical Society. Contemp. Math. 139 (Deodhar, Vinay, eds.), Providence, RI:, 1992, pp. 5-32. MR 94c:55010
  • [D1] Deligne, P., Theoreme de Lefschetz et criteres de degenerescence de suites spectrales, Publ. Math., Inst. Hautes Etud. Sci. 35 (1968), 107-126. MR 39:5582
  • [D2] Deligne, P., Theorie de Hodge. III, Publ. Math., Inst. Hautes Etud. Sci. 44 (1974), 5-77. MR 58:16653b
  • [D3] Deligne, P., Decompositions dans la categorie derivee, Motives. Proceedings of the summer research conference on motives, held at the University of Washington, Seattle, WA, USA, July 20-August 2, 1991. American Mathematical Society. Proc. Symp. Pure Math. 55 (Jannsen, U. et al., eds.), Providence, RI: 1994, pp. 115-128. MR 95h:18013
  • [Gi] Ginzburg, V. A., Equivariant cohomology and Kahler geometry (Russian), Funktsional. Anal. i Prilozhen. 21 (4), 19-34. MR 89b:58013
  • [GKM] Goresky, M.; Kottwitz, R.; MacPherson, R., Equivariant cohomology, Koszul duality, and the localization theorem, Invent. Math. 131 (1) (1998), 25-83. MR 99c:55009
  • [K] Kirwan, F. C., Cohomology of quotients in symplectic and algebraic geometry, Mathematical Notes, vol. 31, Princeton, New Jersey: Princeton University Press, 1984. MR 86i:58050
  • [MW] Maszczyk, T.; Weber, A., Koszul duality for modules over Lie algebra, Duke Math. J. 112 (2002), no. 3, 511-520
  • [VoM] Morel, F.; Voevodsky, V., $A'$-homotopy theory of schemes, Preprint 1998.
  • [Sul] Sullivan, D., Geometric topology. Part I. Localization, periodicity, and Galois symmetry, Massachusetts Institute of Technology, Cambridge, Mass., 1971. MR 58:13006a
  • [Si] Simpson, C., The topological realization of a simplicial presheaf, q-alg/9609004.
  • [Sum] Sumihiro H., Equivariant completions I, Math. Kyoto Univ. 14 (1974), 1-28. MR 49:2732
  • [T] Totaro, B., The Chow ring of a classifying space, math.AG/9802097; Algebraic $K$-theory. Proceedings of an AMS-IMS-SIAM summer research conference, Seattle, WA, USA, July 13-24 1997 Proc. Symp. Pure Math. Vol 67 (Raskind, Wayne et al., eds.), Providence, RI: American Mathematical Society. Proc., 1999, pp. 249-281. MR 2001f:14011

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Additional Information

Andrzej Weber
Affiliation: Institute of Mathematics, Warsaw University, ul. Banacha 2, 02–097 Warszawa, Poland

Keywords: Complete algebraic varieties, equivariant intersection cohomology
Received by editor(s): February 8, 2001
Published electronically: April 23, 2003
Additional Notes: This research was partially supported by grant KBN 2P03A 00218 and by the European Commission RTN Geometric Analysis
Communicated by: Mohan Ramachandran
Article copyright: © Copyright 2003 American Mathematical Society

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