Abstract

Let $X$ be a locally symmetric variety, i.e., the quotient of a bounded symmetric domain by a (say) neat arithmetically-defined group of isometries. Let ${\overline X}^{\rm exc}$ and $X^{{\rm tor,exc}}$ denote its excentric Borel-Serre and toroidal compactifications respectively. We determine their least common modification and use it to prove a conjecture of Goresky and Tai concerning canonical extensions of homogeneous vector bundles. In the process, we see that ${\overline X}^{\rm exc}$ and $X^{{\rm tor,exc}}$ are homotopy equivalent.

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 859-912
Launched on MUSE
2008-08-07
Open Access
No
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