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A note on supersingular abelian varieties
by Chia-Fu Yu  

Vol. 15 No. 1 (2020) P.9~P.32
DOI: https://doi.org/10.21915/BIMAS.2020102
  10.21915/BIMAS.2020102

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].


KEYWORDS
words and phrases.supersingular abelian varieties, Galois descent

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 14K15, 11G10

MILESTONES

Received: 2020-03-12
Revised :
Accepted:


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