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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.

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