On the supersingular locus of Shimura varieties for quaternionic unitary groups

2023/11/30 by Terakado, Yasuhiro, Xue, Jiangwei, Yu, Chia-Fu
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2311.18354

Abstract

We study a Shimura variety attached to a unitary similitude group of a skew-Hermitian form over a totally indefinite quaternion algebra over a totally real number field. We give a necessary and sufficient condition for the existence of skew-Hermitian self-dual lattices. Under this condition we show that the superspecial locus in the fiber at p of the associated Shimura variety is non-empty. We also give an explicit formula for the number of irreducible components of the supersingular locus when p is odd and unramified in the quaternion algebra.

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