Back to Commutative Algebra Seminar: Spring 2022
Commutative Algebra Seminar
Date: Friday, Mar 25, 2022
Time: 2:00PM - 3:00PM
Location: LCB 222
Kevin Tucker
University of Illinois at Chicago
Title |
The Theory of F-rational Signature |
Abstract |
There are a number of invariants defined via Frobenius in the study of singularities in characteristic. One such is the F-signature, which can be viewed as a quantitative measure of F-regularity - an important class of singularities central to the celebrated theory of tight closure pioneered by Hochster and Huneke, and closely related to KLT singularities via standard reduction techniques from characteristic zero. Recently, similar invariants have been introduced as a quantitative measures of F-rationality - another important class of F-singularity closely related to rational singularities in characteristic zero. 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. |
Commutative Algebra