Vol. 6, No. 5, 2012

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Toroidal compactifications of PEL-type Kuga families

Kai-Wen Lan

Vol. 6 (2012), No. 5, 885–966

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.

Kuga families, PEL-type Shimura varieties, degenerations and toroidal compactifications
Mathematical Subject Classification 2000
Primary: 11G18
Secondary: 11G15, 14D06
Received: 23 July 2010
Revised: 15 April 2011
Accepted: 30 June 2011
Published: 31 July 2012
Kai-Wen Lan
Department of Mathematics, Princeton University
and School of Mathematics, Institute for Advanced Study
Princeton, NJ
United States
School of Mathematics
University of Minnesota
Vincent Hall
206 Church Street SE
Minneapolis, MN 55455
United States