Computing abelian varieties over finite fields isogenous to a power

Abstract

In this paper we give a module-theoretic description of the isomorphism classes of abelian varieties $A$ isogenous to $B^r$, where the characteristic polynomial $g$ of Frobenius of $B$ is an ordinary square-free $q$-Weil polynomial, for a power $q$ of a prime $p$, or a square-free $p$-Weil polynomial with no real roots. Under some extra assumptions on the polynomial $g$ we give an explicit description of all the isomorphism classes which can be computed in terms of fractional ideals of an order in a finite product of number fields. In the ordinary case, we also give a module-theoretic description of the polarizations of $A$.

arXiv commentfinal version

References in corpus (3)

• Abelian varieties isogenous to a power of an elliptic curve
• Computing abelian varieties over finite fields isogenous to a power
• Principally polarized squares of elliptic curves with field of moduli equal to Q

Cited by in corpus (4)

• Computing abelian varieties over finite fields isogenous to a power
• Modules over orders, conjugacy classes of integral matrices, and abelian varieties over finite fields
• Products and Polarizations of Super-Isolated Abelian Varieties
• Computing base extensions of ordinary abelian varieties over finite fields