Abstract
We explain how compactications of Kuga families of abelian vari- eties over PEL-type Shimura varieties, including for example all those products of universal abelian schemes, can be constructed (up to good isogenies not af- fecting 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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