On direct and inverse images of \(\mathcal D\)-modules in prime characteristic
type: Item
instance of: scholarly article
title: On direct and inverse images of \(\mathcal D\)-modules in prime characteristic
zbMATH Open document ID: 0673.14012
DOI: 10.1007/BF01246838
author: Burkhard Haastert
published in: Manuscripta Mathematica
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155351
review text: The paper studies the category of modules over the ring of algebraic differential operators on algebraic varieties over a field with finite characteristic. Generalizing the characteristic zero construction, the author defines the functors of direct and inverse images for \({\mathcal D}\)- modules with respect to a morphism \(f:\quad X\to Y\) of smooth varieties. As in the case of characteristic zero, tensoring with the canonical module yields an equivalence between the categories of left and right \({\mathcal D}\)-modules. Finally, an analogy of Kashiwara's equivalence in characteristic \(\neq 0\) is proved, which describes \({\mathcal D}\)-modules with support on a closed subvariety.
Mathematics Subject Classification ID: 14F10
Mathematics Subject Classification ID: 32C38
zbMATH DE Number: 4101355
zbMATH Keywords: algebraic differential operators
zbMATH Keywords: \({\mathcal D}\)-modules
zbMATH Keywords: Kashiwara's equivalence
reviewed by: Valery K. Vedernikov
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4101355