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Local Intersection Cohomology of Baily–Borel Compactifications

Published online by Cambridge University Press:  04 December 2007

M. Goresky ,
G. Harder ,
R. MacPherson  and
A. Nair
M. Goresky
Affiliation:
School of Mathematics, Institute for Advanced Study, 1 Einstein Drive, Princeton, NJ 08540, U.S.A.
G. Harder
Affiliation:
Mathematisches Institut der Universität Bonn, Beringstr asse 1, Zimmer 15, 53115 Bonn, Germany
R. MacPherson
Affiliation:
School of Mathematics, Institute for Advanced Study, 1 Einstein Drive, Princeton, NJ 08540, U.S.A.
A. Nair
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400 005, Bombay, India
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Abstract

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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 cohomologyarithmetic groupintersection cohomologyautomorphic formBaily–Borel
Type
Research Article
Information
Compositio Mathematica , Volume 134 , Issue 3 , December 2002 , pp. 243 - 268
Copyright
© 2002 Kluwer Academic Publishers