Recognizing dualizing complexes

Peter Jørgensen

doi:10.4064/fm176-3-4

Recognizing dualizing complexes

Peter Jørgensen^*

^*Corresponding author af dette arbejde

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avis › Tidsskriftartikel › Forskning › peer review

8 Citationer (Scopus)

Abstract

Let A be a noetherian local commutative ring and let M be a suitable complex of A-modules. It is proved that M is a dualizing complex for A if and only if the trivial extension A ⋉ M is a Gorenstein differential graded algebra. As a corollary, A has a dualizing complex if and only if it is a quotient of a Gorenstein local differential graded algebra.

Originalsprog	Engelsk
Tidsskrift	Fundamenta Mathematicae
Vol/bind	176
Nummer	3
Sider (fra-til)	251-259
Antal sider	9
ISSN	0016-2736
DOI	https://doi.org/10.4064/fm176-3-4
Status	Udgivet - 2003
Udgivet eksternt	Ja

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title = "Recognizing dualizing complexes",

abstract = "Let A be a noetherian local commutative ring and let M be a suitable complex of A-modules. It is proved that M is a dualizing complex for A if and only if the trivial extension A ⋉ M is a Gorenstein differential graded algebra. As a corollary, A has a dualizing complex if and only if it is a quotient of a Gorenstein local differential graded algebra.",

keywords = "Dualizing complex, Dualizing differential graded module, Gorenstein differential graded algebra, Noetherian local commutative ring, Trivial extension",

author = "Peter J{\o}rgensen",

year = "2003",

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language = "English",

volume = "176",

pages = "251--259",

journal = "Fundamenta Mathematicae",

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publisher = "Institute of Mathematics. Polish Academy of Sciences",

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T1 - Recognizing dualizing complexes

AU - Jørgensen, Peter

PY - 2003

Y1 - 2003

N2 - Let A be a noetherian local commutative ring and let M be a suitable complex of A-modules. It is proved that M is a dualizing complex for A if and only if the trivial extension A ⋉ M is a Gorenstein differential graded algebra. As a corollary, A has a dualizing complex if and only if it is a quotient of a Gorenstein local differential graded algebra.

AB - Let A be a noetherian local commutative ring and let M be a suitable complex of A-modules. It is proved that M is a dualizing complex for A if and only if the trivial extension A ⋉ M is a Gorenstein differential graded algebra. As a corollary, A has a dualizing complex if and only if it is a quotient of a Gorenstein local differential graded algebra.

KW - Dualizing complex

KW - Dualizing differential graded module

KW - Gorenstein differential graded algebra

KW - Noetherian local commutative ring

KW - Trivial extension

UR - https://www.scopus.com/pages/publications/0041911567

U2 - 10.4064/fm176-3-4

DO - 10.4064/fm176-3-4

M3 - Journal article

AN - SCOPUS:0041911567

SN - 0016-2736

VL - 176

SP - 251

EP - 259

JO - Fundamenta Mathematicae

JF - Fundamenta Mathematicae

IS - 3

ER -

Recognizing dualizing complexes

Abstract

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