A characteristic-free proof of a basic result on D-modules

Gennady Lyubeznik

doi:10.1016/j.jpaa.2010.11.012

A characteristic-free proof of a basic result on D-modules

Gennady Lyubeznik

Mathematics

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

9 Scopus citations

Abstract

Let k be a field, let R be a ring of polynomials in a finite number of variables over k, let D be the ring of k-linear differential operators of R and let fεR be a non-zero element. It is well-known that Rf, with its natural D-module structure, has finite length in the category of D-modules. We give a characteristic-free proof of this fact. To the best of our knowledge this is the first characteristic-free proof.

Original language	English (US)
Pages (from-to)	2019-2023
Number of pages	5
Journal	Journal of Pure and Applied Algebra
Volume	215
Issue number	8
DOIs	https://doi.org/10.1016/j.jpaa.2010.11.012
State	Published - Aug 2011

Bibliographical note

Funding Information:
NSF support through grants DMS-0202176 and DMS-0701127 is gratefully acknowledged.

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abstract = "Let k be a field, let R be a ring of polynomials in a finite number of variables over k, let D be the ring of k-linear differential operators of R and let fεR be a non-zero element. It is well-known that Rf, with its natural D-module structure, has finite length in the category of D-modules. We give a characteristic-free proof of this fact. To the best of our knowledge this is the first characteristic-free proof.",

author = "Gennady Lyubeznik",

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N2 - Let k be a field, let R be a ring of polynomials in a finite number of variables over k, let D be the ring of k-linear differential operators of R and let fεR be a non-zero element. It is well-known that Rf, with its natural D-module structure, has finite length in the category of D-modules. We give a characteristic-free proof of this fact. To the best of our knowledge this is the first characteristic-free proof.

AB - Let k be a field, let R be a ring of polynomials in a finite number of variables over k, let D be the ring of k-linear differential operators of R and let fεR be a non-zero element. It is well-known that Rf, with its natural D-module structure, has finite length in the category of D-modules. We give a characteristic-free proof of this fact. To the best of our knowledge this is the first characteristic-free proof.

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