A Note on Endomorphisms of Local Cohomology Modules
Waqas Mahmood, Zohaib Zahid

TL;DR
This paper investigates the structure of endomorphism rings of local cohomology modules over local rings, establishing conditions for isomorphisms and extending known results from the case of the ring itself.
Contribution
It provides new sufficient conditions under which the natural homomorphism between endomorphism rings is an isomorphism, extending previous work beyond the case of the ring.
Findings
Identifies conditions for isomorphism of endomorphism rings
Extends known constructions from the ring case to modules
Analyzes homomorphisms between endomorphism rings for different ideals
Abstract
Let denote an ideal of a local ring of dimension . Let denote a finitely generated -module. We study the endomorphism ring of the local cohomology module . In particular there is a natural homomorphism , where denotes the -adic completion functor. We prove sufficient conditions such that it becomes an isomorphism. Moreover, we study a homomorphism of two such endomorphism rings of local cohomology modules for two ideals with the property . Our results extends constructions known in the case of (see e.g. \cite{h1}, \cite{p7}, \cite{p1}).
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