On G-linebundles and \(K_ G^{\bullet}(X)\)
type: Item
instance of: scholarly article
title: On G-linebundles and \(K_ G^{\bullet}(X)\)
zbMATH Open document ID: 0558.14030
author: Knud Lønsted
published in: Journal of Mathematics of Kyoto University
publication date: 1983-01-01T00:00:00Z
review text: Let G be a finite reductive group, acting on an algebraic variety X. The author continues the study of the group \(K_ G(X)\) of G-linearized bundles over X [see \textit{G. Ellingsrud} and the author, Math. Ann. 251, 253-261 (1980; Zbl 0425.14012)]. The main results are the descriptions of \(K_ G(X)\) for the case of dim \(X\leq 1\). If X is a smooth curve and \(B\subset X\) is the ramification locus for the map \(X\to X/G,\) then in \(Pic_ G(X)\) there exists a subgroup \(Pic^ B_ G(X)\) generated by G- invariant divisors with support outside B. It is proved the existence of an equivariant first Chern class from \(Pic^ B_ G(X)\) to \(K_ G(X)\) and equivariant Riemann-Roch formula for line-bundles in \(Pic^ B_ G(X)\). The paper contains interesting examples and discussions.
Mathematics Subject Classification ID: 14L30
Mathematics Subject Classification ID: 14C22
Mathematics Subject Classification ID: 14C40
Mathematics Subject Classification ID: 14C35
Mathematics Subject Classification ID: 14F05
zbMATH DE Number: 3889717
zbMATH Keywords: group action
zbMATH Keywords: K-functor
zbMATH Keywords: Picard group
zbMATH Keywords: G-linearized bundles
zbMATH Keywords: Riemann-Roch formula for line-bundles
reviewed by: A. N. Parshin
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250521434
OpenAlex ID: W1543893468
DOI: 10.1215/KJM/1250521434
description: scientific article; zbMATH DE number 3889717