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arXiv · 2002.10960

Mass formula and Oort's conjecture for supersingular abelian threefolds

Valentijn Karemaker·Fuetaro Yobuko·Chia-Fu Yu
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Abstract

Using the theory of polarised flag type quotients, we determine mass formulae for all principally polarised supersingular abelian threefolds defined over an algebraically closed field $k$ of characteristic $p$. We combine these results with computations of the automorphism groups to study Oort's conjecture; we prove that every generic three-dimensional principally polarised supersingular abelian variety over $k$ of characteristic $\neq 2$ has automorphism group $\{ \pm 1 \}$.

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Valentijn Karemaker, Fuetaro Yobuko, Chia-Fu Yu. 2020-02-25. Mass formula and Oort's conjecture for supersingular abelian threefolds. https://doi.org/10.1016/j.aim.2021.107812

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