DMS Algebra Seminar

Speaker: Thomas Polstra (University of Virginia)

Title: Inversion of Adjunction of $F$-purity

Abstract: Commutative rings of prime characteristic are non-singular if and only if the Frobenius endomorphism is flat. We therefore label prime characteristic singularities by describing the behavior of the Frobenius. For example, rings with the property that the Frobenius is a pure ring homomorphism are called \(F\)-pure. The class of \(F\)-pure rings forms the oldest and one of the fundamental \(F\)-singularity classes. We consider the problem of when a quotient ring of the form \(R/xR\) defines an \(F\)-pure ring. This talk is based on joint work with Austyn Simpson and Kevin Tucker.