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キーワード:
Mathematics, Number Theory
要旨:
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].
