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

Valentijn Karemaker

When is a polarised abelian variety determined by its p-divisible group?
Jeudi, 1 Février, 2024 - 10:30
Résumé : 

We will study the Siegel moduli space of abelian varieties in characteristic p and in particular its supersingular locus. We first determine precisely when this locus is geometrically irreducible. Since it was known that the number of components is a class number, this comes down to solving a “class number one problem” or “Gauss problem”.
Next, we will show when a polarised abelian variety is determined by its p-divisible group. This can be viewed as a Gauss problem for central leaves, which are the loci consisting of points whose associated p-divisible groups are isomorphic. Our solution involves mass formulae, computations of automorphism groups, and a careful analysis of Ekedahl-Oort strata in genus 4.

Institution de l'orateur : 
Utrecht University
Thème de recherche : 
Théorie des nombres
Salle : 
logo uga logo cnrs