Vanishing theorems for constructible sheaves. II
type: Item
instance of: scholarly article
title: Vanishing theorems for constructible sheaves. II
zbMATH Open document ID: 0930.14009
author: Dũng Tráng Lê
author: Helmut A. Hamm
published in: Kodai Mathematical Journal
publication date: 2000-02-14T00:00:00Z
review text: In part I of this paper [J. Reine Angew. Math. 471, 115-138 (1996; Zbl 0876.14012)] the authors proved theorems on the vanishing of higher cohomology of direct images of complexes of constructible sheaves. In this paper they take the ``dual'' point of view and derive results concerning the vanishing of lower cohomology of direct images of such complexes. The main result is a statement which yields lower bounds for the vanishing and applies to \(q\)-complete maps in the sense of Andreotti-Grauert. As an application several very general Lefschetz type theorems and Zariski-Lefschetz type theorems (for open varieties) for the cohomoloyg of constructible sheaves are given. In an appendix a base change theorem for weakly constructible complexes is derived.
Mathematics Subject Classification ID: 14F17
Mathematics Subject Classification ID: 32F10
zbMATH DE Number: 1269770
zbMATH Keywords: \(q\)-complete map
zbMATH Keywords: direct images of complexes
zbMATH Keywords: vanishing of lower cohomology
zbMATH Keywords: Zariski-Lefschetz type theorems
zbMATH Keywords: base change theorem
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2996/kmj/1138043875
OpenAlex ID: W1996509883
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DOI: 10.2996/KMJ/1138043875
description: scientific article; zbMATH DE number 1269770