Séminaire Arithmétique et géométrie algébrique
organisé par l'équipe Arithmétique et géométrie algébrique
Good reduction of Kummer surfaces modulo 2
15 juin 2023 - 14:00Salle de séminaires IRMAIn residue characteristic different from 2, the good reduction of a given Kummer surface is (essentially) equivalent to the good reduction of the abelian surface it is constructed from, and is therefore completely understood via the classical Neron-Ogg-Shafarevich criterion. In residue characteristic 2, however, things are a little bit more interesting, and good reduction of a given abelian surface is not enough to ensure good reduction of its associated Kummer surface. In this talk I will explain a more refined criterion for the good reduction of K3 surfaces in general, and use it to solve the problem of good reduction for Kummer surfaces associated to abelian surfaces with good, non-supersingular reduction in residue characteristic 2. This is joint work with Alexei Skorobogatov.