## STNB2020(34th edition)

### Abelian varieties with everywhere good reduction over certain real quadratic fields

Lassina Dembélé

#### Abstract

A celebrated theorem of Abrashkin-Fontaine asserts that there is no non-zero abelian variety defined over $\mathbf{Q}$ with everywhere good reduction. This result plays a crucial role in the proof of the Serre Conjecture by Khare-Wintenberger. In this talk, we explore the generalisation of this theorem to certain real quadratic fields extending previous results of Schoof and collaborators.