2020 / March Volume 15 No.1
A note on supersingular abelian varieties
| Published Date |
2020 / March
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|---|---|
| Title | A note on supersingular abelian varieties |
| Author | |
| Keyword | |
| Download | |
| Pagination | 9-32 |
| Abstract | In this note we show that every supersingular abelian variety is isogenous to a superspecial abelian variety without increasing field extensions. The proof uses minimal isogenies and Galois descent. We construct a superspecial abelian variety which cannot be descended to a finite field. This answers negatively to a question of the author in [J. Pure Appl. Alg., 2013]. Endomorphism algebras of supersingular elliptic curves over an arbitrary field are investigated. We correct the main result of the author's paper [Math. Res. Let., 2010].
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| DOI | |
| AMS Subject Classification |
14K15, 11G10
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| Received |
2020-03-12
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