Wes Townsend : Second Coefficient Problems in Commutative Algebra

Posted by Wes Townsend , part of the Graduate Algebraic Geometry Seminar.

At

March 1, 2017, 3 p.m.

In

SEO 712

Abstract

The Hilbert-Kunz Function and F-Signature are two key invariants of rings with positive characteristic. In a 2008 paper, Craig Huneke, Paul Monsky, and Moira A. McDermott established a tighter estimate on the asymptotic behavior of the Hilbert-Kunz Function for suitably geometric rings. There are strong connections between the F-Signature and the Hilbert-Kunz Function, but it remains an open question whether it is possible to obtain the same estimates for F-Signature of excellent local normal rings in positive characteristic. We will discuss Huneke, Monsky, and McDermott's result and attempts to extend it to the F-Signature.