Toroidal and reductive Borel-Serre compactifications of locally symmetric spaces
نویسندگان
چکیده
منابع مشابه
On the Reductive Borel-serre Compactification, Iii: Mixed Hodge Structures
We establish a procedure for constructing compatible mixed Hodge structures for the cohomology of various topological compactifications of locally symmetric varieties, notably ones that are not algebraic varieties. This is carried out in full for the case of the reductive Borel-Serre compactification, and conditionally for the excentric compactifications. Introduction. In [BS], Borel and Serre ...
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15 صفحه اولOn the reductive Borel-Serre compactification, II: Excentric quotients and least common modifications
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 X exc and X 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 bundl...
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Here, the left-hand side is the L-cohomology of M with respect to a (locally) invariant metric. Though it would be more natural to allow p = ∞ in Theorem 1, this is not generally possible (see (3.2.2)). On the other hand, there is a natural mapping H (∞)(M) → H • (p)(M) when p < ∞, because M has finite volume. The definition of M is recalled in (1.9). Theorem 1 can be viewed as an analogue of t...
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ژورنال
عنوان ژورنال: American Journal of Mathematics
سال: 1999
ISSN: 1080-6377
DOI: 10.1353/ajm.1999.0032