On the reductive Borel-Serre compactification: $L^p$-cohomology of arithmetic groups (for large $p$)
| dc.creator | Zucker, Steven | |
| dc.date | 2007-04-11 | |
| dc.date.accessioned | 2026-07-07T07:56:06Z | |
| dc.date.available | 2026-07-07T07:56:06Z | |
| dc.description | The $L^2$-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.description | 32 pages | |
| dc.identifier | https://arxiv.org/abs/0704.1335 | |
| dc.identifier | http://arxiv.org/abs/0704.1335 | |
| dc.identifier | Amer. J. Math. 123 (2001), 951-984 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/127186 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Algebraic Topology | |
| dc.title | On the reductive Borel-Serre compactification: $L^p$-cohomology of arithmetic groups (for large $p$) | |
| dc.type | text |