Seminario Dottorato: From Shafarevich's conjecture to finite flat group schemes

Wednesday 23 February 2011 - Hendrik Verhoek

ARGOMENTI: Seminari Dottorato

Wednesday 23 February 2011 h. 14:30, room 2BC30
Hendrik Verhoek (Roma 2)
"From Shafarevich's conjecture to finite flat group schemes"

I will give an introduction to, and overview of, the work of Fontaine, Abrashkin, Schoof, Brumer-Kramer and Calegari that came forth from Shafarevich's conjecture or question about the non-existence of non-zero abelian varieties over Q with everywhere good reduction. First I briefly discuss what this conjecture is about. Then we will see the work of the pioneers Fontaine and Abrashkin passing by: they independently proved there does not exist such an abelian variety. After that we will consider the work of Schoof, Brumer and Kramer and Calegari related to abelian varieties over Q with so called semi-stable reduction at some places. Finally I will say something about generalizations and open problems.

Rif. int. C. Marastoni, T. Vargiolu

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