The Gersten conjecture for Witt groups in the equicharacteristic case
type: Item
instance of: scholarly article
title: The Gersten conjecture for Witt groups in the equicharacteristic case
zbMATH Open document ID: 1015.19002
author: Paul Balmer
author: Stefan G. Gille
author: Ivan Panin
author: Charles Walter
published in: Documenta Mathematica
publication date: 2003-07-15T00:00:00Z
full work available at URL: https://eudml.org/doc/122734
full work available at URL: 10.html
review text: For an \(n\)-dimensional regular local ring \(R\) write \(X\) for the spectrum of \(R\) and \(X^{(p)}\) for the primes of height \(p\). The Gersten-Witt complex connects the Witt groups of the residue fields at points in \(X^{(i)}\) and \(X^{(i+1)}\). The augmented Gersten-Witt complex, \(\text{GWC}_a(R)\), is the Gersten-Witt complex augmented by the natural map \(W(R) \rightarrow W(K)\), where \(K\) is the field of fractions of \(R\). The main result of the paper asserts that \(\text{GWC}_a(R)\) is exact for any regular local ring containing some field (equicharacteristic regular local ring). The bulk of the paper consists of explanations how the results in the existing literature are going to be used, and then the proof of the main result is given without much effort on less than one printed page.
Mathematics Subject Classification ID: 19G12
Mathematics Subject Classification ID: 18E30
zbMATH DE Number: 1862887
zbMATH Keywords: Witt group
zbMATH Keywords: Gersten conjecture
zbMATH Keywords: triangulated categories
zbMATH Keywords: equicharacteristic
reviewed by: Kazimierz Szymiczek
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1862887