Théorème de dualité pour la cohomologie locale au bord des ouverts fortement pseudoconvexes. (Duality theorem for local cohomology at the boundary of strongly pseudoconvex open sets)
type: Item
instance of: scholarly article
title: Théorème de dualité pour la cohomologie locale au bord des ouverts fortement pseudoconvexes. (Duality theorem for local cohomology at the boundary of strongly pseudoconvex open sets)
zbMATH Open document ID: 0586.32015
author: Tosiaki Kori
published in: Hokkaido Mathematical Journal
publication date: 1981-01-01T00:00:00Z
review text: Let D be a relatively compact open set of a complex manifold M of dimension n (n\(\geq 2)\) such that the boundary \(\partial D=B\) is a smooth strongly pseudoconvex \({\mathcal C}^{\infty}\) manifold. For \({\mathcal F}^ a \)coherent analytic sheaf on M the author proves the following results: \((1)\quad \dim_{{\mathbb{C}}}H^ q(B;\underline H^ 1_ B({\mathcal F}))<\infty\) for \(0<q<prof {\mathcal F}-1;\) (2) the spaces \(H^ q(B;\underline H^ 1_ B({\mathcal F}))\) and \(Ext^{n-1-q}(B;\underline H^ 1_ B({\mathcal F}),\underline H^ 1_ B(\Omega^ n))\) are dual topological vector spaces for \(q<prof {\mathcal F}-1.\) These results are the analogues for the sheaf \b{H}\({}^ 1_ B({\mathcal F})\) of the results of A. Andreotti and H. Grauert for (1) and of B. Malgrange and J.-P. Serre for (2). The techniques are standard.
Mathematics Subject Classification ID: 32C37
Mathematics Subject Classification ID: 32C36
Mathematics Subject Classification ID: 32T99
Mathematics Subject Classification ID: 14B15
zbMATH DE Number: 3939699
zbMATH Keywords: duality theorem
zbMATH Keywords: local cohomology
zbMATH Keywords: pseudoconvex manifold
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3939699