On the reductive Borel-Serre compactification, II: excentric quotients and least common modifications

• Autores: Steven Zucker
• Localización: American journal of mathematics, ISSN 0002-9327, Vol. 130, Nº 4, 2008, págs. 859-912
• Idioma: inglés
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• Resumen

  • 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.