On algebraic \(K\)-theory of real algebraic varieties with circle action
type: Item
instance of: scholarly article
title: On algebraic \(K\)-theory of real algebraic varieties with circle action
zbMATH Open document ID: 1044.14033
DOI: 10.1016/S0022-4049(01)00129-3
author: Yildiray Ozan
published in: Journal of Pure and Applied Algebra
publication date: 2002-06-24T00:00:00Z
review text: Let \(X\) be a compact, connected, orientable, nonsingular algebraic variety endowed with an algebraic free action of \(S^1\). Assume that \(Y=X/S^{1}\) is a real algebraic variety. The main result of the paper is that the projection \({\pi}: X \rightarrow Y\) induces a surjective map on reduced algebraic \(K\)-groups tensored with \(\mathbb Q\); i.e, the map \({\pi}^{*} :{\tilde K}_0({\mathcal R}(Y,{\mathbb C}))\otimes {\mathbb Q} \rightarrow {\tilde K}_0({\mathcal R}(X,{\mathbb C}))\otimes {\mathbb Q}\) is onto, where \({\mathcal R}(X,{\mathbb C})= {\mathcal R}(X)\otimes {\mathbb C}\) and \({\mathcal R}(X)\) denotes the ring of entire rational functions on the variety \(X.\) This result partially extends the Bochnak-Kucharz result that \({\tilde K}_0({\mathcal R}(X\times S^{1},{\mathbb C})) = {\tilde K}_0({\mathcal R}(X,{\mathbb C}))\) for any real algebraic variety.
reviewed by: Piotr Krasoń
Mathematics Subject Classification ID: 14P25
Mathematics Subject Classification ID: 19E08
Mathematics Subject Classification ID: 13D15
Mathematics Subject Classification ID: 19L64
Mathematics Subject Classification ID: 19A31
Mathematics Subject Classification ID: 14C35
zbMATH DE Number: 1758364
zbMATH Keywords: real algebraic variety
zbMATH Keywords: \(S^{1}\)-action
zbMATH Keywords: algebraic \(K\)-groups
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1758364