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Fall and Winter 2016 On the injective dimension of $\mathscr{F}$-finite modules and holonomic $\mathscr{D}$-modules
Mehdi Dorreh
Illinois J. Math. 60(3-4): 819-831 (Fall and Winter 2016). DOI: 10.1215/ijm/1506067293

Abstract

Let $R$ be a regular local ring containing a field $k$ of characteristic $p$ and $M$ be an $\mathscr{F}$-finite module. In this paper, we study the injective dimension of $M$. We prove that $\operatorname{dim}_{R}(M)-1\leq\operatorname{inj.dim}_{R}(M)$. If $R=k[[x_{1},\ldots,x_{n}]]$ where $k$ is a field of characteristic $0$ we prove the analogous result for a class of holonomic $\mathscr{D}$-modules which contains local cohomology modules.

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Mehdi Dorreh. "On the injective dimension of $\mathscr{F}$-finite modules and holonomic $\mathscr{D}$-modules." Illinois J. Math. 60 (3-4) 819 - 831, Fall and Winter 2016. https://doi.org/10.1215/ijm/1506067293

Information

Received: 16 October 2016; Revised: 16 April 2017; Published: Fall and Winter 2016
First available in Project Euclid: 22 September 2017

zbMATH: 06790329
MathSciNet: MR3705446
Digital Object Identifier: 10.1215/ijm/1506067293

Subjects:
Primary: 13N10
Secondary: 13D45

Rights: Copyright © 2016 University of Illinois at Urbana-Champaign

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Vol.60 • No. 3-4 • Fall and Winter 2016
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