Mathematical Research Letters

Volume 18 (2011)

Number 5

Elevators for Degenerations of Pel Structures

Pages: 889 – 907

DOI: http://dx.doi.org/10.4310/MRL.2011.v18.n5.a7

Author

Kai-Wen Lan

Abstract

We show that the maximal rank of mixed characteristic degenerations of abelian varieties parameterized by a PEL-type Shimura variety are the same as the maximal rank of equicharacteristic zero degenerations (of abelian varieties parameterized by the same Shimura variety). As a byproduct, we obtain a simple proof of Yasuo Morita’s conjecture in 1975 that an abelian variety with additional structures parameterized by a compact PEL-type Shimura variety has potential good reductions everywhere.

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