Event Type
Seminar
Monday, January 25, 2021 12:30 PM
Will Sawin (Columbia University)

Abstract: Faltings proved the statement, previously conjectured by
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.