Vanishing of local cohomology and set-theoretically Cohen–Macaulay ideals

Majid Eghbali; Alberto F. Boix

doi:10.1007/s12215-022-00821-z

Vanishing of local cohomology and set-theoretically Cohen–Macaulay ideals

Majid Eghbali, Alberto F. Boix

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

Abstract

In this paper, first, we generalize a result of Peskine–Szpiro on the relation between the cohomological dimension and projective dimension. Then, we give conditions for the vanishing of local cohomology from local to global and vice versa. Our final goal in the present paper is to examine the set-theoretically Cohen–Macaulay ideals to find some cohomological characterization of these kinds of ideals.

Original language	English
Journal	Rendiconti del Circolo Matematico di Palermo
DOIs	https://doi.org/10.1007/s12215-022-00821-z
State	Accepted/In press - 1 Jan 2022
Externally published	Yes

Keywords

Cohomological dimension
Linkage
Local cohomology
Projective dimension
Ring endomorphism
Set-theoretically Cohen–Macaulay ideals

ASJC Scopus subject areas

Mathematics (all)

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10.1007/s12215-022-00821-z

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abstract = "In this paper, first, we generalize a result of Peskine–Szpiro on the relation between the cohomological dimension and projective dimension. Then, we give conditions for the vanishing of local cohomology from local to global and vice versa. Our final goal in the present paper is to examine the set-theoretically Cohen–Macaulay ideals to find some cohomological characterization of these kinds of ideals.",

keywords = "Cohomological dimension, Linkage, Local cohomology, Projective dimension, Ring endomorphism, Set-theoretically Cohen–Macaulay ideals",

author = "Majid Eghbali and Boix, {Alberto F.}",

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AU - Boix, Alberto F.

N1 - Funding Information: The authors contributed equally to this work. To the soul of professor Wolfgang Vogel. A. F. Boix was partially supported by the Spanish Ministry of Science and Innovation Grant PID2019–104844GB–I00. Publisher Copyright: © 2022, The Author(s), under exclusive licence to Springer-Verlag Italia S.r.l., part of Springer Nature.

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N2 - In this paper, first, we generalize a result of Peskine–Szpiro on the relation between the cohomological dimension and projective dimension. Then, we give conditions for the vanishing of local cohomology from local to global and vice versa. Our final goal in the present paper is to examine the set-theoretically Cohen–Macaulay ideals to find some cohomological characterization of these kinds of ideals.

AB - In this paper, first, we generalize a result of Peskine–Szpiro on the relation between the cohomological dimension and projective dimension. Then, we give conditions for the vanishing of local cohomology from local to global and vice versa. Our final goal in the present paper is to examine the set-theoretically Cohen–Macaulay ideals to find some cohomological characterization of these kinds of ideals.

KW - Cohomological dimension

KW - Linkage

KW - Local cohomology

KW - Projective dimension

KW - Ring endomorphism

KW - Set-theoretically Cohen–Macaulay ideals

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ER -

Vanishing of local cohomology and set-theoretically Cohen–Macaulay ideals

Abstract

Keywords

ASJC Scopus subject areas

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