Dimension formulas for the hyperfunction solutions to holonomic \(\mathcal D\)-modules
type: Item
instance of: scholarly article
title: Dimension formulas for the hyperfunction solutions to holonomic \(\mathcal D\)-modules
zbMATH Open document ID: 1066.32014
DOI: 10.1016/S0001-8708(02)00099-3
author: Kiyoshi Takeuchi
published in: Advances in Mathematics
publication date: 2004-01-06T00:00:00Z
review text: In the theory of constructible sheaves, as presented by \textit{M. Kashiwara} and \textit{P. Shapira} [cf. their book ``Sheaves on manifolds'' (Grundlehren der Mathematischen Wissenschaften 292, Berlin: Springer Verlag) (1990; Zbl 0709.18001)], a dimension formula is given for the hyperfunction solutions to a certain class of holonomic \({\mathcal D}\)-modules: \[ \dim^{\mathbb{C}}\Hom_{{\mathcal D}_X}({\mathcal M},{\mathcal B}_M)_0= \sum^N_{i=1} \text{mult}_{T^*_{X_i}X}({\mathcal M}) \] for a sheaf \({\mathcal D}_X\) of partial differential operators with holomorphic coefficients on \(X=\) complexification of \(M\), and \({\mathcal M}\) a coherent \({\mathcal D}_X\)-module. The proof is based on index theorems for constructible sheaves. For detailed definitions cf. [\textit{M. Kashiwara}, Systems of microdifferential equations, Progress in Mathematics 34 (Birkhäuser, Boston) (1983; Zbl 0521.58057)].
reviewed by: Alfred Aeppli
Mathematics Subject Classification ID: 32C38
Mathematics Subject Classification ID: 35A27
zbMATH DE Number: 2022085
zbMATH Keywords: \(\mathcal D\)-module
zbMATH Keywords: Holonomic system
zbMATH Keywords: Index theorem
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2022085