Local cohomology and Lyubeznik numbers of F-pure rings

Abstract

In this article, we study certain local cohomology modules over F-pure rings. We give sufficient conditions for the vanishing of some Lyubeznik numbers, derive a formula for computing these invariants when the F-pure ring is standard graded and, by its means, we provide some new examples of Lyubeznik tables. We study associated primes of certain Ext-modules, showing that they are all compatible ideals. Finally, we focus on properties that Lyubeznik numbers detect over a globally F-split projective variety.