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arXiv · 1910.06519

Supersingular loci of some Shimura varieties for CM unitary groups

Maria Fox
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Abstract

In this note, we study Shimura varieties for the groups $\mathrm{GU}(V)$, where $V$ is a Hermitian space relative to a CM extension $E/E^+$. We give a description of the supersingular locus of the fiber at a prime $\nu$ over $p$ of such a Shimura variety, under the assumptions that $\mathrm{dim}_E(V) \leq 4$ and that the prime $p$ splits completely in $E^+$ and is unramified in $E$.

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Maria Fox. 2019-10-15. Supersingular loci of some Shimura varieties for CM unitary groups. https://arxiv.org/abs/1910.06519

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