Virtual Commutative Algebra Seminar
Friday, 3 February, 2023, 6.30 pm
Host: J. K. Verma
Venue: meet.google.com/exp-duym-nrr
Speaker: Kevin Tucker
Affiliation: University of Illinois Chicago, IL, USA
Title: The Theory of F-rational Signature
Abstract: The celebrated results of Smith, Hara, and Mehta-Srinivas connect rational singularities in characteristic zero after reduction to characteristic p > 0 with F-rational singularities. In recent years, a number of invariants defined via Frobenius in positive characteristics have been introduced as quantitative measures of F-rationality. These include the F-rational signature (Hochster-Yao), relative F-rational signature (Smirnov-Tucker), and dual F-signature (Sannai). In this talk, I will discuss new results in joint work with Smirnov relating each of these invariants. In particular, we show that the relative F-rational signature and dual F-signature coincide, while also verifying that the dual F-signature limit converges.