Abstract

The L2-cohomology of an arithmetic quotient of an Hermitian symmetric space (i.e., of a locally symmetric variety) is known to have the topological interpretation as the intersection homology of its Baily-Borel Satake compactification. In this article, we observe that even without the Hermitian hypothesis, the Lp-cohomology of an arithmetic quotient, for p finite and sufficiently large, is isomorphic to the ordinary cohomology of its reductive Borel-Serre compactification. We use this to generalize a theorem of Mumford concerning homogeneous vector bundles, their invariant Chern forms and the canonical extensions of the bundles; here, though, we are referring to canonical extensions to the reductive Borel-Serre compactification of any arithmetic quotient. To achieve that, we give a systematic discussion of vector bundles and Chern classes on stratified spaces.

pdf

Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 951-984
Launched on MUSE
2001-10-01
Open Access
No
Back To Top

This website uses cookies to ensure you get the best experience on our website. Without cookies your experience may not be seamless.