Faithfulness of Top Local Cohomology Modules in Domains

TL;DR

This paper investigates when the top local cohomology module of a domain is faithful over the ring, providing conditions especially in positive prime characteristic cases.

Contribution

It establishes that the top local cohomology module is faithful when the cohomological dimension equals the number of generators of the ideal in positive prime characteristic.

Findings

Faithfulness of top local cohomology modules under certain conditions

Verification in positive prime characteristic cases

Connection between generators of ideal and cohomology faithfulness

Abstract

We study the conditions under which the highest nonvanishing local cohomology module of a domain $R$ with support in an ideal $I$ is faithful over $R$, i.e., which guarantee that $H^c_I(R)$ is faithful, where $c$ is the cohomological dimension of $I$. In particular, we prove that this is true for the case of positive prime characteristic when $c$ is the number of generators of $I$.