Eric Canton : Characterizing F-singularities using log discrepancies of semivaluations

Posted by Wenliang Zhang , part of the Commutative Algebra Seminar.

At

Oct. 17, 2016, 1 p.m.

In

SEO 427

Abstract

We have long known, or implicitly used, that to a potential splitting \phi of the Frobenius homomorphism on a ring R of positive characteristic one can assign a divisor on Spec(R), and these divisors describe the Frobenius splitting behavior of \phi at height one primes. We generalize this process and assign coefficients called log discrepancies to valuations on Spec(R/P) for primes P of R. Using these log discrepancies, we can characterize the Frobenius splitting behavior of \phi at any point of Spec(R).