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September 2020 A new outlook on cofiniteness
Kamran Divaani-Aazar, Hossein Faridian, Massoud Tousi
Kyoto J. Math. 60(3): 1033-1045 (September 2020). DOI: 10.1215/21562261-2021-0007

Abstract

Let a be an ideal of a commutative Noetherian (not necessarily local) ring R . In the case cd ( a , R ) 1 , we show that the subcategory of a -cofinite R -modules is Abelian. Using this fact and the technique of way-out functors, we show that, if cd ( a , R ) 1 , or if dim ( R / a ) 1 , or if dim ( R ) 2 , then the local cohomology module H a i ( X ) is a -cofinite for every R -complex X with finitely generated homology modules and every i Z . We further answer Hartshorne’s Question 1.3 in the three aforementioned cases, and we reveal a correlation between his Questions 1.1, 1.2, and 1.3.

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Kamran Divaani-Aazar. Hossein Faridian. Massoud Tousi. "A new outlook on cofiniteness." Kyoto J. Math. 60 (3) 1033 - 1045, September 2020. https://doi.org/10.1215/21562261-2021-0007

Information

Received: 4 May 2017; Revised: 29 November 2017; Accepted: 1 March 2018; Published: September 2020
First available in Project Euclid: 12 August 2020

MathSciNet: MR4134357
Digital Object Identifier: 10.1215/21562261-2021-0007

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

Rights: Copyright © 2020 Kyoto University

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Vol.60 • No. 3 • September 2020
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