Algebraic Geometry Seminar

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Reduction of Brauer Classes on K3 Surfaces, with Applications to Rationality Problems

Speaker: Anthony Várilly-Alvarado, Rice University

Location: Warren Weaver Hall 512

Date: Tuesday, April 30, 2024, 3:30 p.m.

Synopsis:

Given a K3 surface X over a number field k and a Brauer class A on X, what can we say about the set of primes good reduction of X at which A vanishes? We show that this set contains a set of positive natural density when X is a very general K3 surface. If X is special, this set can have density 0 (although it is often infinite, by work of Maulik and Tayou). We use this result to show there exist conjecturally irrational cubic fourfolds that have rational mod p specializations at a set of primes of positive natural density.  This is joint work with Sarah Frei and Brendan Hassett.