An analogue of holonomic \(D\)-modules on smooth varieties in positive characteristics
type: Item
instance of: scholarly article
title: An analogue of holonomic \(D\)-modules on smooth varieties in positive characteristics
zbMATH Open document ID: 1003.32002
published in: Homology, Homotopy and Applications
publication date: 2002-08-01T00:00:00Z
full work available at URL: https://eudml.org/doc/49679
full work available at URL: volume4-2-1.htm
review text: Let \(X\) be a smooth variety over a field \(K\) with \(\text{char} (K)= p>0\) and \(D_X\) the ring of Grothendieck differential operators on \(X\). In this paper the author defines and studies a very nice category of \(D_X\)-modules called filtration holonomic modules. This is a modification of the same-name concept introduced by the same author [\textit{R. Bögvad}, J. Algebra 173, 638-667 (1995; Zbl 0845.14014)]. The modified definition is motivated by its usefulness and stability with respect to the usual operations. He proves that this category is closed under \(D_X\)-module extensions, submodules and quotient modules and preserved by direct and inverse images and by local cohomology. Furthermore, every filtration holonomic module has a finite decomposition series.
reviewed by: E. Ballico
Mathematics Subject Classification ID: 32C38
Mathematics Subject Classification ID: 14F10
Mathematics Subject Classification ID: 16S32
zbMATH DE Number: 1770068
zbMATH Keywords: ring of differential operators
zbMATH Keywords: positive characteristics
zbMATH Keywords: holonomic
zbMATH Keywords: \(F\)-finite module
author: Rikard Bøgvad
MaRDI profile type: Publication
OpenAlex ID: W2047444786
DOI: 10.4310/HHA.2002.V4.N2.A5
description: scientific article; zbMATH DE number 1770068