Sam Shideler : Hilbert-Kunz Multiplicity and the F-Signature

Posted by Samuel Shideler , part of the Graduate Algebraic Geometry Seminar.

At

Sept. 9, 2015, 3 p.m.

In

SEO 712

Abstract

I will discuss two characteristic $p$ invariants of a ring $R$ - the Hilbert-Kunz multiplicity $e_{HK}(R)$ and the F-signature $s(R)$. Both are invariants defined using Frobenius that give information about the singularities of $R$. I will prove basic facts about these invariants, discuss their computations, and give a broad overview of known results and further questions. The talk will primarily follow the survey article by Huneke with the same title.