Austyn Simpson : F-injectivity, cohomological fullness, and the deformation problem

Posted by Kevin Tucker , part of the Algebraic Geometry Seminar.

At

April 29, 2026, 3 p.m.

In

1227 SEO

Abstract

Given a local ring R of prime characteristic and a nonzero divisor x such that R/xR is F-injective, it is a longstanding open problem to determine whether R must itself be F-injective. There are partial affirmative results that rely on R/xR being cohomologically full, while examples of F-injective rings which lack this property are very sparse. In this talk I will describe a family of such examples which are geometrically normal over an F-finite field, and discuss potential implications for the deformation problem. I will also highlight a feature of these rings which distinguishes them from Du Bois singularities in characteristic zero. Joint with A. De Stefani and T. Polstra.