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arXiv · 1412.7107

A note on supersingular abelian varieties

Chia-Fu Yu
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Abstract

In this note we show that any supersingular abelian variety is isogenous to a superspecial abelian variety without increasing field extensions. The proof uses minimal isogenies and the Galois descent. We then construct a superspecial abelian variety which not directly defined over a finite field. This answers negatively to a question of the author [J. Pure Appl. Alg., 2013] concerning of endomorphism algebras occurring in Shimura curves. Endomorphism algebras of supersingular elliptic curves over an arbitrary field are also investigated. We correct a main result of the author's paper [Math. Res. Let., 2010].

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Chia-Fu Yu. 2017-06-10. A note on supersingular abelian varieties. https://arxiv.org/abs/1412.7107

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