Duality for Koszul homology over Gorenstein rings

Claudia Miller; Hamidreza Rahmati; Janet Striuli

doi:10.1007/s00209-013-1202-5

Duality for Koszul homology over Gorenstein rings

Claudia Miller, Hamidreza Rahmati, Janet Striuli

Department of Mathematics

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

Abstract

We study Koszul homology over local Gorenstein rings. It is well known that if an ideal is strongly Cohen-Macaulay the Koszul homology algebra satisfies Poincaré duality. We prove a version of this duality which holds for all ideals and allows us to give two criteria for an ideal to be strongly Cohen-Macaulay. The first can be compared to a result of Hartshorne and Ogus; the second is a generalization of a result of Herzog, Simis, and Vasconcelos using sliding depth.

Original language	English (US)
Pages (from-to)	329-343
Number of pages	15
Journal	Mathematische Zeitschrift
Volume	276
Issue number	1-2
DOIs	https://doi.org/10.1007/s00209-013-1202-5
State	Published - Feb 2014

Keywords

Gorenstein ring
Poincaré duality
Strongly Cohen-Macaulay ideals

ASJC Scopus subject areas

General Mathematics

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10.1007/s00209-013-1202-5

Cite this

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title = "Duality for Koszul homology over Gorenstein rings",

abstract = "We study Koszul homology over local Gorenstein rings. It is well known that if an ideal is strongly Cohen-Macaulay the Koszul homology algebra satisfies Poincar{\'e} duality. We prove a version of this duality which holds for all ideals and allows us to give two criteria for an ideal to be strongly Cohen-Macaulay. The first can be compared to a result of Hartshorne and Ogus; the second is a generalization of a result of Herzog, Simis, and Vasconcelos using sliding depth.",

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author = "Claudia Miller and Hamidreza Rahmati and Janet Striuli",

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T1 - Duality for Koszul homology over Gorenstein rings

AU - Miller, Claudia

AU - Rahmati, Hamidreza

AU - Striuli, Janet

PY - 2014/2

Y1 - 2014/2

N2 - We study Koszul homology over local Gorenstein rings. It is well known that if an ideal is strongly Cohen-Macaulay the Koszul homology algebra satisfies Poincaré duality. We prove a version of this duality which holds for all ideals and allows us to give two criteria for an ideal to be strongly Cohen-Macaulay. The first can be compared to a result of Hartshorne and Ogus; the second is a generalization of a result of Herzog, Simis, and Vasconcelos using sliding depth.

AB - We study Koszul homology over local Gorenstein rings. It is well known that if an ideal is strongly Cohen-Macaulay the Koszul homology algebra satisfies Poincaré duality. We prove a version of this duality which holds for all ideals and allows us to give two criteria for an ideal to be strongly Cohen-Macaulay. The first can be compared to a result of Hartshorne and Ogus; the second is a generalization of a result of Herzog, Simis, and Vasconcelos using sliding depth.

KW - Gorenstein ring

KW - Poincaré duality

KW - Strongly Cohen-Macaulay ideals

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JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

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ER -

Duality for Koszul homology over Gorenstein rings

Abstract

Keywords

ASJC Scopus subject areas

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