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arXiv · 1703.10076

Fully maximal and fully minimal abelian varieties

Valentijn Karemaker·Rachel Pries
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Abstract

We introduce and study a new way to catagorize supersingular abelian varieties defined over a finite field by classifying them as fully maximal, mixed, or fully minimal. The type of $A$ depends on the normalized Weil numbers of $A$ and its twists. We analyze these types for supersingular abelian varieties and curves under conditions on the automorphism group. In particular, we present a complete analysis of these properties for supersingular elliptic curves and supersingular abelian surfaces in arbitrary characteristic, and for a one-dimensional family of supersingular curves of genus $3$ in characteristic $2$.

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Valentijn Karemaker, Rachel Pries. 2017-03-29. Fully maximal and fully minimal abelian varieties. https://arxiv.org/abs/1703.10076

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