Mathematical Research Letters

Volume 24 (2017)

Number 2

Support of local cohomology modules over hypersurfaces and rings with FFRT

Pages: 401 – 420

DOI: http://dx.doi.org/10.4310/MRL.2017.v24.n2.a7

Authors

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

Luis Núñez-Betancourt (Matemáticas Básicas, Centro de Investigación en Matemáticas, Guanajuato, Gto., México)

Abstract

Let $(R, m, K)$ be a local ring and $I$ be an ideal. It is conjectured that the local cohomology modules $H^i_I (R)$ have closed support on $\textrm{Spec }R$. We establish this conjecture for hypersurface rings in positive characteristic. In addition, we prove that the associated primes of $H^i_I (R)$ are finite for rings with finite $F$-representation type. As a consequence, $H^i_I (R)$ has finitely many associated primes for a Stanley–Reisner ring, $R$, over any field of positive characteristic. In addition, we present results in a similar direction for certain determinantal rings.

Full Text (PDF format)

The first author was partially supported by the NSF Grant 1401384.

The second author was partially supported by the NSF Grant 1502282.

Received 21 February 2016

Published 24 July 2017