I am interested in studying some algorithmic aspects of hyperelliptic curves on finite fields. For this I have studied the topics of Projective model of hyperelliptic curves, Local rings and Noetherian rings, Valuation at a point on a curve, Field of functions for genus, Divisors, Group of divisor classes, Jacobian, Munford representation, Cantor algorithm , Fast Arithmetic, Torsion Subgroups, 2-Torsion of the Jacobian, 3-Torsion.
Now I want to study abelian varieties, in order to study isogenies and more specifically a type of isogenies, but I can't find a text with a basic definition of an abelian variety, or how to define it for finite fields, in addition, a concept of polarization arises. that I have not understood very well, any suggestion or way to address these issues in a way that is oriented to the algorithmic part?