100, rue des maths 38610 Gières / GPS : 45.193055, 5.772076 / Directeur : Louis Funar

Stefano Marseglia

Computing isomorphism classes and polarisations of abelian varieties over finite fields
Mardi, 12 Décembre, 2023 - 16:00
Résumé : 

We consider abelian varieties over a finite field which are ordinary, or over a prime field, and which have commutative endomorphism algebra.
Works of Deligne and Centeleghe-Stix allow us to describe these abelian varieties in terms of fractional ideals of an order in an étale algebra. I will explain how such descriptions can be exploited to explictly compute the abelian varieties up to isomorphism.
Moreover, results by Howe give us a way to compute principal polarisations of the abelian varieties in the ordinary case. In a joint work with Bergström and Karemaker we extend these results to the prime field case.

Thème de recherche : 
Théorie des nombres
Salle : 
logo uga logo cnrs