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arXiv · 2208.07809

Lifts of supersingular abelian varieties with small Mumford-Tate groups

Yeuk Hay Joshua Lam·Abhishek Oswal
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Abstract

We investigate to what extent an abelian variety over a finite field can be lifted to one in characteristic zero with small Mumford-Tate group. We prove that supersingular abelian surfaces, respectively threefolds, can be lifted to ones isogenous to a square, respectively product, of elliptic curves. On the other hand, we show that supersingular abelian threefolds cannot be lifted to one isogenous to the cube of an elliptic curve over the Witt vectors.

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Yeuk Hay Joshua Lam, Abhishek Oswal. 2022-08-16. Lifts of supersingular abelian varieties with small Mumford-Tate groups. https://arxiv.org/abs/2208.07809

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