Finiteness of Associated Primes of Local Cohomology Modules Over Stanley-Reisner Rings

TL;DR

This paper proves that local cohomology modules over Stanley-Reisner rings with a T-space simplicial complex have finitely many associated primes, addressing a key question about their structure.

Contribution

It establishes the finiteness of associated primes for local cohomology modules over a specific class of Stanley-Reisner rings, a previously unresolved problem.

Findings

Finiteness of associated primes proven for local cohomology over certain Stanley-Reisner rings

Results apply when the simplicial complex is a T-space

Advances understanding of local cohomology module structure

Abstract

Local cohomology modules, even over a Noetherian ring $R$, are typically unwieldly. As such, it is of interest whether or not they have finitely many associated primes. We prove the affirmative in the case where $R$ is a Stanley-Reisner ring over a field, whose associated simplicial complex is a $T$-space.