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Local Intersection Cohomology of Baily�CBorel Compactifications |
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| Authors: | M. Goresky G. Harder R. MacPherson A. Nair |
| Affiliation: | (1) Institute for Advanced Study, School of Mathematics, 1 Einstein Drive, Princeton, NJ, 08540, U.S.A;(2) Mathematisches Institut der Universität Bonn, Beringstr asse 1, Zimmer 15, 53115 Bonn, Germany;(3) Institute for Advanced Study, School of Mathematics, 1 Einstein Drive, Princeton, NJ, 08540, U.S.A;(4) Tata Institute of Fundamental Research, School of Mathematics, Homi Bhabha Road, Mumbai, 400 005 Bombay, India |
| Abstract: | The local intersection cohomology of a point in the Baily–Borel compactification (of a Hermitian locally symmetric space) is shown to be canonically isomorphic to the weighted cohomology of a certain linear locally symmetric space (an arithmetic quotient of the associated self-adjoint homogeneous cone). Explicit computations are given for the symplectic group in four variables. |
| Keywords: | weighted cohomology arithmetic group intersection cohomology automorphic form Baily– Borel |
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