Rigidity for equivariant \(K\)-theory
type: Item
instance of: scholarly article
title: Rigidity for equivariant \(K\)-theory
zbMATH Open document ID: 1187.19004
author: Serge Yagunov
author: Paul Arne Østvær
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2009-12-22T00:00:00Z
review text: The authors extend the classical rigidity results for algebraic \(K\)-theory with torsion coefficients to the equivariant setting of linear algebraic group actions. These results concern rigidity for rational points, field extensions, and Hensel local rings. Let \(G\) be a linear algebraic group over an infinite field \(k\). Let \(V\) be a \(G\)-equivariant separated \(k\)-scheme of finite type. Let \(n>0\) be prime to the characteristic of \(k\). It is shown that \(K_*(V\times_k - ;\mathbb Z/n)\) defines a functor `with weak transfers' on the category of smooth quasi projective \(k\)-schemes. The rigidity results follow.
reviewed by: Wilberd van der Kallen
Mathematics Subject Classification ID: 19D99
Mathematics Subject Classification ID: 19L47
zbMATH DE Number: 5651244
zbMATH Keywords: equivariant
zbMATH Keywords: weak transfer
zbMATH Keywords: rigidity
zbMATH Keywords: Hensel
zbMATH Keywords: Bott element
MaRDI profile type: Publication
full work available at URL: j.crma.2009.10.020
OpenAlex ID: W2050295989
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DOI: 10.1016/J.CRMA.2009.10.020
description: scientific article; zbMATH DE number 5651244