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On the existence of abelian surfaces with everywhere good reduction

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Lassina Dembele
University of Warwick/MPIM
Wed, 2017-03-01 14:15 - 15:15
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

A famous result of Fontaine (and Abrashkin) states that there is no abelian variety over the rationals
with everywhere good reduction. Fontaine's proof of this result relies on the non-existence of certain
finite flat group schemes. His technique has been refined by several people (including Schoof, Brumer
and Calegari) to prove non-existence of semi-stable abelian varieties over various fields. On the other
hand, a result of More-Bailly states that in every genus $g$, there is a curve of genus $g$ with everywhere
good reduction over ${Z}$. So, as the base field varies, we must hope to find more abelian varieties
with trivial conductor.

In this talk, I will some existence results for abelian surfaces with everywhere good reduction over
real quadratic fields.

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