A note on Bockstein homomorphisms in local cohomology

Abstract

This note is an exposition on the results from [SiW] related to Lyubeznik's conjecture on local cohomology. We use the method of Bockstein homomorphisms, which to our knowledge has not been employed before in commutative algebra. As an example, we strengthen the classical Stanley–Reisner correspondence by relating Bockstein homomorphisms on local cohomology in monomial rings to the topological Bockstein homomorphisms of simplicial complexes.

We introduce the necessary language in Section 1, then present the motivation with our main theorem in Section 2, and finally illustrate our results in the case of Stanley–Reisner ideals in Section 3.