On an endomorphism ring of local cohomology
Majid Eghbali, Peter Schenzel

TL;DR
This paper investigates the structure and endomorphism ring of the top local cohomology module in cases where the Hartshorne-Lichtenbaum Vanishing Theorem does not hold, revealing new insights into its algebraic properties.
Contribution
It provides a detailed analysis of the endomorphism ring of local cohomology modules when the vanishing theorem fails, including a key isomorphism for complete rings.
Findings
Endomorphism ring structure characterized in non-vanishing cases.
Established isomorphism between $H^d_I(R)$ and $H^d_{rak m}(R/J)$ for complete rings.
Connectedness properties related to the structure of local cohomology modules.
Abstract
Let be an ideal of a local ring with For the local cohomology module it is a well-known fact that it vanishes for and is an Artinian -module for In the case that the Hartshorne-Lichtenbaum Vanishing Theorem fails, that is we explore its fine structure. In particular, we investigate its endomorphism ring and related connectedness properties. In the case is complete we prove - as a technical tool - that for a certain ideal Thus, properties of and its Matlis dual might be described in terms of the local cohomology supported in the maximal ideal.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Algebraic Geometry and Number Theory · Homotopy and Cohomology in Algebraic Topology
