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arXiv · 2311.18354

On the supersingular locus of Shimura varieties for quaternionic unitary groups

Yasuhiro Terakado·Jiangwei Xue·Chia-Fu Yu
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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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Yasuhiro Terakado, Jiangwei Xue, Chia-Fu Yu. 2023-11-30. On the supersingular locus of Shimura varieties for quaternionic unitary groups. https://arxiv.org/abs/2311.18354

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