On the spectrum representing algebraic \(K\)-theory for a finite field
type: Item
instance of: scholarly article
title: On the spectrum representing algebraic \(K\)-theory for a finite field
zbMATH Open document ID: 0585.55001
author: B. George
published in: Osaka Journal of Mathematics
publication date: 1985-01-01T00:00:00Z
review text: Let \({\mathbb Z}\times \text{BGL}{\mathbb F}^+_ r\) be the representing space for the algebraic \(K\)-theory of a field with \(r\) elements. Let \(p\) be an odd prime such that \(r\) generates \(({\mathbb Z}/p^ 2)^*\). Let \(A\) denote the spectrum obtained by \(p\)-localisation from \(K{\mathbb F}_ r\). The author computes \(H^*(A; {\mathbb Z}/p)\) and \(H_*(A; {\mathbb Z}/p).\) Let \(G\) be the ring spectra resulting from Adam's splitting \[ bu_{(p)}=\bigvee^{p- 1}_{j=1}\Sigma^{2(j-1)} G. \] The \(G\)-module action on \(A\) and Quillen's fibre sequence \(A\to^{n}G\to^{\theta}G\) are used to analyze the ring \(A_*({\mathbb C}P^{\infty})\).
Mathematics Subject Classification ID: 55N15
Mathematics Subject Classification ID: 18F25
Mathematics Subject Classification ID: 55R35
Mathematics Subject Classification ID: 55P42
zbMATH DE Number: 3938026
zbMATH Keywords: localization
zbMATH Keywords: representing space for the algebraic \(K\)-theory of a field
reviewed by: Victor P. Snaith
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3938026