Vanishing in highest degree for solutions of D-modules and perverse sheaves
type: Item
instance of: scholarly article
title: Vanishing in highest degree for solutions of D-modules and perverse sheaves
zbMATH Open document ID: 0728.58037
author: Pierre Schapira
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 1990-01-01T00:00:00Z
review text: Let M be a real analytic manifold of dimension n, X a complexification of M, \({\mathcal D}_ x\) the sheaf of differential operators on X, \({\mathcal E}_ x\) the sheaf on \(T^*X\) of (finite order) microdifferential operators and \({\mathcal M}\) a coherent module over the sheaf of rings \({\mathcal E}_ x.\) The author proves the vanishing of \({\mathcal E}xt^ j_{{\mathcal E}_ x}({\mathcal M},{\mathcal C}_ M)\) for \(j\geq n\), where \({\mathcal C}_ M\) denotes the sheaf of Sato's microfunctions. In particular, he obtains for coherent \({\mathcal D}_ x\)-modules \({\mathcal M}\) that \({\mathcal E}xt^ j_{{\mathcal D}_ x}({\mathcal M},{\mathcal B}_ M)=0\) for \(j\geq n\), where \({\mathcal B}_ M\) is the sheaf of Sato's hyperfunctions.
reviewed by: Sorin Popescu
Mathematics Subject Classification ID: 58J15
Mathematics Subject Classification ID: 32C38
Mathematics Subject Classification ID: 32L20
Mathematics Subject Classification ID: 32A45
Mathematics Subject Classification ID: 32C05
zbMATH DE Number: 4203329
zbMATH Keywords: \({\mathcal D}\)-modules
zbMATH Keywords: perverse sheaves
zbMATH Keywords: microdifferential operators
zbMATH Keywords: Sato's microfunctions
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195170962
OpenAlex ID: W2089880523
cites work: Q3320507
cites work: On the maximally overdetermined system of linear differential equations. I
cites work: On holonomic systems of microdifferential equations. III: Systems with regular singularities
cites work: Q3717382
cites work: Q4403324
cites work: Q3216881
cites work: Q3213885
DOI: 10.2977/PRIMS/1195170962
description: scientific article; zbMATH DE number 4203329