Appears in collection : Stefano Marseglia: Ideal Class Monoid and Computing Abelian Varieties over Finite Fields

The aim of this course is to describe an algorithm that given an isogeny class of abelian varieties over Fq returns the isomorphism classes within it. The main tool is that, under certain hypotheses on the isogeny class, we can functorially describe the abelian varieties in terms of fractional ideals of orders in étale algebras over Q (product of number fields).