On the reductive Borel-Serre compactification: $L^p$-cohomology of arithmetic groups (for large $p$)

dc.creatorZucker, Steven
dc.date2007-04-11
dc.date.accessioned2026-07-07T07:56:06Z
dc.date.available2026-07-07T07:56:06Z
dc.descriptionThe $L^2$-cohomology 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 $L^p$-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
dc.description32 pages
dc.identifierhttps://arxiv.org/abs/0704.1335
dc.identifierhttp://arxiv.org/abs/0704.1335
dc.identifierAmer. J. Math. 123 (2001), 951-984
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/127186
dc.subjectAlgebraic Geometry
dc.subjectAlgebraic Topology
dc.titleOn the reductive Borel-Serre compactification: $L^p$-cohomology of arithmetic groups (for large $p$)
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