Annihilators of local cohomology modules and simplicity of rings of differential operators

Alberto F. Boix; Majid Eghbali

doi:10.1007/s13366-018-0396-4

Annihilators of local cohomology modules and simplicity of rings of differential operators

Alberto F. Boix, Majid Eghbali

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

11 Scopus citations

Abstract

One classical topic in the study of local cohomology is whether the non-vanishing of a specific local cohomology module is equivalent to the vanishing of its annihilator; this has been studied by several authors, including Huneke, Koh, Lyubeznik and Lynch. Motivated by questions raised by Lynch and Zhang, the goal of this paper is to provide some new results about this topic, which provide some partial positive answers to these questions. The main technical tool we exploit is the structure of local cohomology as module over rings of differential operators.

Original language	English
Pages (from-to)	665-684
Number of pages	20
Journal	Beitrage zur Algebra und Geometrie
Volume	59
Issue number	4
DOIs	https://doi.org/10.1007/s13366-018-0396-4
State	Published - 1 Nov 2018
Externally published	Yes

Keywords

Annihilators
Local cohomology

ASJC Scopus subject areas

Algebra and Number Theory
Geometry and Topology

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10.1007/s13366-018-0396-4

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abstract = "One classical topic in the study of local cohomology is whether the non-vanishing of a specific local cohomology module is equivalent to the vanishing of its annihilator; this has been studied by several authors, including Huneke, Koh, Lyubeznik and Lynch. Motivated by questions raised by Lynch and Zhang, the goal of this paper is to provide some new results about this topic, which provide some partial positive answers to these questions. The main technical tool we exploit is the structure of local cohomology as module over rings of differential operators.",

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AB - One classical topic in the study of local cohomology is whether the non-vanishing of a specific local cohomology module is equivalent to the vanishing of its annihilator; this has been studied by several authors, including Huneke, Koh, Lyubeznik and Lynch. Motivated by questions raised by Lynch and Zhang, the goal of this paper is to provide some new results about this topic, which provide some partial positive answers to these questions. The main technical tool we exploit is the structure of local cohomology as module over rings of differential operators.

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Annihilators of local cohomology modules and simplicity of rings of differential operators

Abstract

Keywords

ASJC Scopus subject areas

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