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

2010/04/23 by Gennady Lyubeznik, Lyubeznik, Gennady
Computer Science · Mathematics · #13N10 #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AC #msc:13N10

paper · pdf · doi:10.48550/arxiv.1004.4225

8 pages

arxiv created 2010/04/23 · openalex publication_date 2010/04/23 · arxiv updated 2010/04/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 f be a non-zero element of R. It is well-known that R_f, 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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