On the associated primes of Matlis duals of local cohomology modules II

TL;DR

This paper investigates the associated primes of Matlis duals of local cohomology modules, providing partial answers to open questions and supporting a conjecture, while also establishing some non-finiteness results.

Contribution

It combines existing ideas to address open questions about associated primes of MDLCMs and offers new non-finiteness results for local cohomology modules.

Findings

Partial answers to open questions on associated primes of MDLCMs.

Support for the conjecture on the set of associated primes of MDLCMs.

New non-finiteness results for local cohomology modules.

Abstract

In continuation of [1] we study associated primes of Matlis duals of local cohomology modules (MDLCM). We combine ideas from Helmut Z\"oschinger on coassociated primes of arbitrary modules with results from [1], [4], [5], [6] and obtain partial answers to questions which were left open in [1]. These partial answers give further support for conjecture $(*)$ from [1] on the set of associated primes of MDLCMs. In addition, and also inspired by ideas from Z\"oschinger, we prove some non-finiteness results of local cohomology.