Mathematical Research Letters

Volume 27 (2020)

Number 6

Faithfulness of top local cohomology modules in domains

Pages: 1755 – 1765

DOI: https://dx.doi.org/10.4310/MRL.2020.v27.n6.a7

Authors

Melvin Hochster (Department of Mathematics, University of Michigan, Ann Arbor, Mich., U.S.A.)

Jack Jeffries (Department of Mathematics, University of Nebraska, Lincoln, Neb., U.S.A.)

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 $I$.

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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