On Endomorphism Rings of Local Cohomology Modules

TL;DR

This paper investigates the structure of endomorphism rings of local cohomology modules over Cohen-Macaulay rings, establishing isomorphisms under specific cohomological conditions.

Contribution

It proves that the natural homomorphism to the endomorphism ring is an isomorphism for cohomologically complete intersection ideals, extending understanding of local cohomology modules.

Findings

Isomorphism of endomorphism rings for certain local cohomology modules

Results hold for Matlis duals of local cohomology modules

Applicable to Cohen-Macaulay local rings with specific ideal conditions

Abstract

Let I be an ideal of a Complete Cohen-Macaulay local ring R of dimension n. We wil show that the natural homomorphism Rto HomR(HcI(KR), HcI(KR)) is an isomorphism provided that I is a cohomologically compltete intersection ideal of grade c where KR (resp. HiI(.)) denote the canonical module (resp. i-th local cohomology with respect to the ideal I) of R. The same result is true for the Matlis dual of HcI(KR).