Cookies

We use cookies to ensure that we give you the best experience on our website. You can change your cookie settings at any time. Otherwise, we'll assume you're OK to continue.

Department of Mathematical Sciences

Seminar Archives

On this page you can find information about seminars in this and previous academic years, where available on the database.

Arithmetic Study Group: An informal introduction to the Shafarevich Conjecture

Presented by Victor Abrashkin, Durham University

14 October 2008 14:15 in CM 101

The Shafarevich Conjecture pertains to the non-existence of abelian varieties over $\Bbb Q$ with everywhere good reduction. We discuss its generalization to proper smooth schemes over $\Bbb Z$ (i.e. projective varieties over $\Bbb Q$ with everywhere good reduction) and recent progress towards varieties which have bad semi-stable reduction in p=3 and good reduction in all $p\ne 3$. Main attention will be paid to the roles of finite flat group schemes, crystalline and semi-stable representations on the one side and of Odlyzko estimates for minimal discriminants of algebraic number fields on the other side.

Contact pankaj.vishe@durham.ac.uk or athanasios.bouganis@durham.ac.uk for more information