Anna Brosowsky : The Cartier core map for Cartier algebras

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

At

Oct. 18, 2022, 11 a.m.

In

636 SEO

Abstract

For a local $F$-finite ring, the splitting prime is an "obstruction" to strong $F$-regularity. In this talk, we will define the self-map on the Frobenius split locus of a ring $R$ which sends a point $P$ to the splitting prime of $R_P$, and discuss the generalization of this map to the setting of Cartier algebras. We will go over some properties of this map and, as an application, will show how it behaves for Stanley-Reisner rings.