Contents Online
Mathematical Research Letters
Volume 18 (2011)
Number 5
Elevators for Degenerations of Pel Structures
Pages: 889 – 907
DOI: https://dx.doi.org/10.4310/MRL.2011.v18.n5.a7
Author
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.
Published 28 October 2011