Karl Schwede : Singularities in mixed characteristic via perfectoid big Cohen-Macaulay algebras

Posted by Kevin Tucker , part of the Commutative Algebra Seminar.

At

Oct. 8, 2018, 3 p.m.

In

612 SEO

Abstract

I will discuss applications of the existence and functoriality of big Cohen-Macaulay algebras (due to Andre, Gabber and others) to study singularities in mixed characteristic. In particular, we introduce analogs of rational/F-rational and log terminal/F-regular singularities in mixed characteristic and study their properties. As an application, we will obtain new results on F-rationality and F-regularity as the characteristic varies.