The Witt group of a smooth complex surface
type: Item
instance of: scholarly article
title: The Witt group of a smooth complex surface
zbMATH Open document ID: 0641.14004
DOI: 10.1007/BF01458327
author: Fernando Fernández-Carmena
published in: Mathematische Annalen
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164261
review text: In Math. Ann. 277, 453-468 (1987; see the preceding review) [see also the correction thereof, ibid. 280, No.4, 697-698 (1988)], the author established an exact sequence \[ 0\quad \to \quad W(X)\quad \to \quad W(K)\quad \to \coprod_{co\dim (x)=1}W(k(x)), \] where X is a smooth surface over a field k (char(k)\(\neq 2)\), K is the function field, k(x) is the residue field at \(x\in X\) and \(W(\quad)\) is the Witt ring functor. This sequence is used to determine W(X), where X is a smooth surface over \({\mathbb{C}}\). Relations with K-theory and étale cohomology are discussed.
reviewed by: Niels Schwartz
Mathematics Subject Classification ID: 14C35
Mathematics Subject Classification ID: 14F05
Mathematics Subject Classification ID: 11E16
Mathematics Subject Classification ID: 14A15
Mathematics Subject Classification ID: 14H99
zbMATH DE Number: 4043984
zbMATH Keywords: Witt group of a smooth complex curve
zbMATH Keywords: Witt group of a smooth complex surface
zbMATH Keywords: K-theory
zbMATH Keywords: étale cohomology
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4043984