Barcelona Fall Workshop on Number Theory II

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

Presenters

L. Dembélé (Luxembourg)

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.

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