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.

引用

页码：885 / 966

页数：82

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