Isogenies of certain abelian varieties over finite fields with p-ranks zero

01/01/2020

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by   Steve Thakur, et al.

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We study the isogenies of certain abelian varieties over finite fields with non-commutative endomorphism algebras with a view to potential use in isogeny-based cryptography. In particular, we show that any two such abelian varieties with endomorphism rings maximal orders in the endomorphism algebra are linked by a cyclic isogeny of prime degree.