Mathematical Research Letters
Volume 27 (2020)
Faithfulness of top local cohomology modules in domains
Pages: 1755 – 1765
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 $I$.
The first-named author was partially supported by National Science Foundation grants DMS–1401384 and DMS–1902116.
The second-named author was partially supported by National Science Foundation grant DMS–1606353.
Received 19 September 2019
Accepted 20 November 2019
Published 17 February 2021