Über Differentialoperatoren und \({\mathcal D}\)-Moduln in positiver Charakteristik. (On differential operators and \({\mathcal D}\)- modules in positive characteristic)
type: Item
instance of: scholarly article
title: Über Differentialoperatoren und \({\mathcal D}\)-Moduln in positiver Charakteristik. (On differential operators and \({\mathcal D}\)- modules in positive characteristic)
zbMATH Open document ID: 0607.14010
DOI: 10.1007/BF01277602
author: Burkhard Haastert
published in: Manuscripta Mathematica
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155229
review text: This paper is about differential operators and \({\mathcal D}\)-modules on a smooth variety over a field of prime characteristic. Beilinson and Bernstein called a (smooth) variety \({\mathcal D}\)-affine, if every \({\mathcal D}\)-module is generated by global sections and all its higher cohomology groups vanish. They showed, that all flag manifolds over a field of characteristic \(0\) are \({\mathcal D}\)-affine. A smooth variety is called \({\mathcal D}\)-quasi-affine, if every \({\mathcal D}\)- module is generated by global sections. Beside some generalities the main results of the article under consideration are the \({\mathcal D}\)-affinity of the projective space, the \({\mathcal D}\)-quasi-affinity of the ordinary flag manifolds (G/B) and the \({\mathcal D}\)-affinity of the ordinary flag manifold of \(Sl_ 3\) (over a field of prime characteristic). In contrast to characteristic \(0\) generally there exists some non-vanishing higher cohomology group of the associated graded algebra gr(\({\mathcal D})\) on an ordinary flag manifold.
Mathematics Subject Classification ID: 14F10
Mathematics Subject Classification ID: 14M15
zbMATH DE Number: 3981329
zbMATH Keywords: \({\mathcal D}\)-quasi affine variety
zbMATH Keywords: \({\mathcal D}\)-module
zbMATH Keywords: flag manifolds
zbMATH Keywords: non- vanishing higher cohomology group
zbMATH Keywords: flag manifold
MaRDI profile type: Publication
cites work: Cohomology of induced representations for algebraic groups
cites work: Q3933105
cites work: On the Dimension of Modules and Algebras IX: Direct Limits
cites work: Differential operators on homogeneous spaces. III: Characteristic varieties of Harish Chandra modules and of primitive ideals
cites work: Über Bahnen und deren Deformationen bei linearen Aktionen reduktiver Gruppen
cites work: Kazhdan-Lusztig conjecture and holonomic systems
cites work: On the Homological Dimension of Algebras of Differential Operators
cites work: A Mackey imprimitivity theory for algebraic groups
cites work: Q3328651
cites work: Q3755566
cites work: Q3877891
cites work: Q4143433
cites work: Ample subvarieties of algebraic varieties. Notes written in collaboration with C. Musili
cites work: Modular representations of classical Lie algebras and semi-simple groups
cites work: Über Darstellungen höherer Frobenius-Kerne halbeinfacher algebraischer Gruppen
cites work: The global homological dimension of the ring of differential operators on a nonsingular variety over a field of positive characteristic
description: scientific article; zbMATH DE number 3981329