Title: Reduction of Brauer Classes on Surfaces, with Applications to Rationality Problems
Speaker: Anthony Várilly-Alvarado
Speaker Info: Rice University
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Special Note:
Abstract:
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. We use this result to show there exist very general cubic fourfolds, which are conjecturally irrational, 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.Date: Tuesday, May 03, 2022