The construction of weight-two arithmetic cohomology
type: Item
instance of: scholarly article
title: The construction of weight-two arithmetic cohomology
zbMATH Open document ID: 0615.14004
DOI: 10.1007/BF01405097
author: Stephen Lichtenbaum
published in: Inventiones Mathematicae
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/143450
review text: One constructs for any regular noetherian scheme X a two-term complex \(\Gamma\) (2,X) of sheaves in the étale topology which is acyclic outside of [1,2] and whose hypercohomology sheaves \({\mathcal H}^ 1\) and \({\mathcal H}^ 2\) are related to the algebraic K-theory as classical cohomology is related to topological K-theory. In specific situations these \({\mathcal H}^ i\) have arithmetic properties. The construction solves at weight-two level a conjecture done by Beilinson for Zariski topology and extended by the author to the étale topology and moreover completed with arithmetic features.
Mathematics Subject Classification ID: 14C35
Mathematics Subject Classification ID: 18F25
zbMATH DE Number: 3995852
zbMATH Keywords: dilogarithm
zbMATH Keywords: hypercohomology sheaves
zbMATH Keywords: algebraic K-theory
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3995852