I would like to advertise this talk in the **Stanford AG Seminar**.

Will Sawin – The Shafarevich Conjecture for Hypersurfaces in Abelian Varieties

Time: Mar 27, 2020 07:00 PM Eastern Time (US and Canada)

To join the zoom meeting please email me and I will send you the link.

Abstract: Faltings proved the statement, previously conjectured by Shafarevich, that there are finitely many abelian varieties of dimension n, defined over the rational numbers (or another fixed number field), with good reduction outside a fixed finite set of primes, up to isomorphism. In joint work with Brian Lawrence, we prove an analogous finiteness statement for hypersurfaces in a fixed abelian variety with good reduction outside a finite set of primes. I will give a broad, intuitive introduction to some of the ideas in the proof, which combines tools from different areas in algebraic geometry, arithmetic geometry, and number theory, and builds heavily on recent work of Lawrence and Venkatesh.