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Seminar

# The Shafarevich Conjecture for Hypersurfaces in Abelian Varieties

Speaker

Will Sawin (Columbia University)

Date

Mon, Jan 25 2021, 12:30pm

Location

Zoom

Shafarevich, that there are finitely many abelian varieties of

dimension n, defined over a 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 introduction to some of the

ideas in the proof, which builds on p-adic Hodge theory techniques

from work of Lawrence and Venkatesh as well as a little-known field of

algebraic geometry.