Gersten's conjecture for some complexes of vanishing cycles
type: Item
instance of: scholarly article
title: Gersten's conjecture for some complexes of vanishing cycles
zbMATH Open document ID: 0827.19002
DOI: 10.1007/BF02568202
author: Ofer Gabber
published in: Manuscripta Mathematica
publication date: 1995-11-28T00:00:00Z
full work available at URL: https://eudml.org/doc/156026
review text: \textit{S. Bloch} and \textit{A. Ogus} noticed, on the second half of page 190 of their paper ``Gersten's conjecture and the homology of schemes'' [Ann. Sci. Éc. Norm. Supér., IV. Sér. 7, 181-201 (1974; Zbl 0307.14008)], that the proof of their main theorem (which is a cohomological version of Gersten's conjecture in \(K\)-theory; for the latter see the Proceedings of the Summer 1972 Seattle Conference [\textit{S. M. Gersten}, Lect. Notes Math. 341, 211-243 (1973; Zbl 0289.18011)]) follows from the vanishing of a certain map -- in fact this reduction was discovered by Quillen in his proof, ``in some important equi-characteristic cases'', of Gersten's conjecture [\textit{D. Quillen}, Lect. Notes Math. 341, 85-147 (1973; Zbl 0292.18004)]. -- In the paper under review a strengthened version of the Bloch-Ogus observation is proved and also, therefore, a cohomological version of Gersten's conjecture. The author remarks that his proof -- which is too technical to be described here -- ``may apply to \(p\)-adic vanishing cycles and theories satisfying the same formalism''.
Mathematics Subject Classification ID: 19E08
Mathematics Subject Classification ID: 14C25
Mathematics Subject Classification ID: 14F20
Mathematics Subject Classification ID: 19E15
Mathematics Subject Classification ID: 19E20
zbMATH DE Number: 724662
zbMATH Keywords: sheaves
zbMATH Keywords: cohomology
zbMATH Keywords: \(p\)-adic vanishing cycles
zbMATH Keywords: \(K\)-theory
zbMATH Keywords: schemes
zbMATH Keywords: Gersten conjecture
Wikidata QID: Q123244366
reviewed by: Sebastian Xambó
MaRDI profile type: Publication
cites work: Gersten's conjecture and the homology of schemes
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description: scientific article; zbMATH DE number 724662