Commutative Algebra Seminar

Title

Quasi-F-Purity, F-Pure Thresholds, and Arithmetic Supersingularity

Abstract

A weakening of Frobenius splitting, Quasi-F-Splittings have proven to be a vital invariant in the study of varieties in positive characteristic, with numerous applications to arithmetic and birational geometry. This weaker condition extends the application of Frobenius to study singularities of arithmetically supersingular varieties, encompassing a much broader class of examples. In this talk I’ll provide an overview of Quasi-F-Splittings and introduce a local analogue, Quasi-F-Purity. I will also discuss how quasi-F-pure hypersurfaces are “as close to being F-pure as possible” by computing the F-pure threshold of an arbitrary quasi-F-pure hypersurface.

This talk includes joint work with Jack J Garzella.