Toroidal compactifications of PEL-type Kuga families

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Abstract

We explain how compactifications of Kuga families of abelian varieties over PEL-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.

Original languageEnglish (US)
Pages (from-to)885-966
Number of pages82
JournalAlgebra and Number Theory
Volume6
Issue number5
DOIs
StatePublished - 2012

Keywords

  • Degenerations and toroidal compactifications
  • Kuga families
  • PEL-type Shimura varieties

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