Toroidal compactifications of PEL-type Kuga families

被引：23
|
作者：
Lan, Kai-Wen [1 ,2 ]
机构：
[1] Princeton Univ, Dept Math, Princeton, NJ 08544 USA
[2] Inst Adv Study, Sch Math, Princeton, NJ 08540 USA
来源：
ALGEBRA & NUMBER THEORY | 2012年 / 6卷 / 05期
基金：
美国国家科学基金会;
关键词：
Kuga families; PEL-type Shimura varieties; degenerations and toroidal compactifications; ALGEBRAIC VARIETY; SINGULARITIES; CONSTRUCTION; COHOMOLOGY; RESOLUTION; MODULI; SPACES; FIELD;
D O I：
10.2140/ant.2012.6.885
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We explain how compactifications of Kuga families of abelian varieties over PELq-type Shimura varieties, including for example all those products of universal abelian schemes, can be constructed (up to good isogenies not affecting the relative cohomology) by a uniform method. We also calculate the relative cohomology and explain its various properties crucial for applications to the cohomology of automorphic bundles.
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页码：885 / 966
页数：82
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