Cohomologically Cofinite Complexes

Marco Porta; Liran Shaul; Amnon Yekutieli

doi:10.1080/00927872.2013.822506

Cohomologically Cofinite Complexes

Marco Porta, Liran Shaul, Amnon Yekutieli

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

17 Scopus citations

Abstract

Let A be a commutative noetherian ring, and 𝔞 an ideal in it. In this paper we continue the study, begun in [11], of the derived 𝔞-adic completion and the derived 𝔞-torsion functors. Here are our results: (1) a structural characterization of bounded above cohomologically complete complexes; (2) the Cohomologically Complete Nakayama Theorem; and (3) a characterization of cohomologically cofinite complexes.

Original language	English
Pages (from-to)	597-615
Number of pages	19
Journal	Communications in Algebra
Volume	43
Issue number	2
DOIs	https://doi.org/10.1080/00927872.2013.822506
State	Published - 1 Feb 2015

Keywords

Adic completion
Derived functors
Torsion

ASJC Scopus subject areas

Algebra and Number Theory

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10.1080/00927872.2013.822506

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AU - Shaul, Liran

AU - Yekutieli, Amnon

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N2 - Let A be a commutative noetherian ring, and 𝔞 an ideal in it. In this paper we continue the study, begun in [11], of the derived 𝔞-adic completion and the derived 𝔞-torsion functors. Here are our results: (1) a structural characterization of bounded above cohomologically complete complexes; (2) the Cohomologically Complete Nakayama Theorem; and (3) a characterization of cohomologically cofinite complexes.

AB - Let A be a commutative noetherian ring, and 𝔞 an ideal in it. In this paper we continue the study, begun in [11], of the derived 𝔞-adic completion and the derived 𝔞-torsion functors. Here are our results: (1) a structural characterization of bounded above cohomologically complete complexes; (2) the Cohomologically Complete Nakayama Theorem; and (3) a characterization of cohomologically cofinite complexes.

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KW - Derived functors

KW - Torsion

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JF - Communications in Algebra

IS - 2

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Cohomologically Cofinite Complexes

Abstract

Keywords

ASJC Scopus subject areas

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