The goal of this talk is to discuss a solution to Grothendieck's problem regarding the cohomological dimension of an ideal in a regular local ring. For this, we will define a new invariant called `F-depth' using the Frobenius action on the local cohomology modules. We will start by briefly reviewing the theory of F-modules, as the proofs borrow ideas from this theory. This talk will be based on Section 4 of Lyubeznik's paper.
