Tue, March 24, 2026
3:00 pm - 4:00 pm
Cockins Hall - CH228
Sarah Frei
Rice University
Title
Rationality in arithmetic families
Abstract
The rationality problem in algebraic geometry asks whether a given algebraic variety can be parameterized by algebraic functions. A natural question in the study of rationality is the following: is rationality a deformation invariant in smooth families? In arithmetic families, this question asks how the rationality of a variety defined over Q interacts with the rationality of its modulo p reductions for various primes p. In this talk, I'll discuss work in progress with Asher Auel and Alena Pirutka on algebraic varieties over Q that are not rational over the complex numbers but are rational modulo p for infinitely many primes p.