Spring 2023 ATTACHED PRIMES OF LOCAL COHOMOLOGY MODULES OF COMPLEXES
Nguyen Minh Tri
J. Commut. Algebra 15(1): 75-83 (Spring 2023). DOI: 10.1216/jca.2023.15.75

Abstract

Let (R,𝔪) be a local ring, 𝒵 a specialization closed subset of Spec R and X an R-complex with finitely generated homology and finite dimension. We show that

AttRH𝒵dimX(X)={𝔭SuppRXcd(𝒵,R𝔭)infX𝔭=dimRX}.

We also present a generalization of the Lichtenbaum–Hartshorne vanishing theorem for complexes of R-modules.

Citation

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Nguyen Minh Tri. "ATTACHED PRIMES OF LOCAL COHOMOLOGY MODULES OF COMPLEXES." J. Commut. Algebra 15 (1) 75 - 83, Spring 2023. https://doi.org/10.1216/jca.2023.15.75

Information

Received: 13 August 2020; Revised: 16 July 2021; Accepted: 17 July 2021; Published: Spring 2023
First available in Project Euclid: 20 June 2023

MathSciNet: MR4604787
zbMATH: 07725176
Digital Object Identifier: 10.1216/jca.2023.15.75

Subjects:
Primary: 13D45
Secondary: 13D07 , 13D09

Keywords: Attached primes , derived category , Lichtenbaum–Hartshorne vanishing theorem , local cohomology

Rights: Copyright © 2023 Rocky Mountain Mathematics Consortium

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Vol.15 • No. 1 • Spring 2023
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