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arXiv · 2609.04072

Oort's conjecture for split unitary Shimura varieties

Paul Philippe·Fabian Schnelle·Eva Viehmann
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Abstract

We prove that generically on the basic stratum of split unitary Shimura varieties, the universal abelian variety with endomorphism structure and polarization has automorphism group $\{\pm 1\}$, except for a few degenerate cases. This is a direct analogue of Oort's conjecture on automorphisms of supersingular abelian varieties. On the way, we explicitly compute the generic automorphism group of the universal $p$-divisible group in a given basic isogeny class.

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Paul Philippe, Fabian Schnelle, Eva Viehmann. 2026-09-03. Oort's conjecture for split unitary Shimura varieties. https://arxiv.org/abs/2609.04072

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