Commutative Algebra Seminar

Title

Using F -modules to measure singularities

Abstract

F-modules were introduced by Lyubeznik in order to study properties of local cohomology modules in positive characteristic. Since then, F-modules have been found to have different applications in commutative algebra and algebraic geometry.

The goal of this talk is twofold. First, to show how (certain) F-modules can be used to recover invariants associated to the singularities of a hypersurface in positive characteristic. And, secondly, to produce two new families of ideals for measuring singularities, the so called F-jumping and F-Jacobian ideals.