Topological models for arithmetic
type: Item
instance of: scholarly article
title: Topological models for arithmetic
zbMATH Open document ID: 0792.19003
DOI: 10.1016/0040-9383(94)90032-9
author: Eric M. Friedlander
author: William Dwyer
published in: Topology
publication date: 1994-07-25T00:00:00Z
review text: A ``good \(\text{mod } \ell\) model'' \(X^ A\) for the etale topological type of a commutative ring \(A\) is found in certain cases. Thus, (1) If \(A= \mathbb{Z}[1/ \ell]\) for an odd regular prime \(\ell\), \(X^ A= \mathbb{R} P^ \alpha\vee S^ 1\). (2) If \(A\) is a coordinate ring of a suitable affine curve over \(\mathbb{F}_ q\), then \(X^ A\) is a fibration over \(S^ 1\) with fiber the \(p\)- completion of a finite wedge of circles. (3) If \(A\) is a generalized local field of transcendence degree \(r\) over \(\mathbb{F}_ q\), \(X^ A\) is a fibration over \(S^ 1\) with fibre the \(p\)- completion of a product of \(r\) circles. Secondly, the etale \(K\)-theory space of \(X^ A\) in case (1) has a cohomology which injects into the cohomology of the algebraic \(K\)-theory space of \(A\). Corollaries depending on the validity of the Lichtenbaum- Quillen conjecture are then derived.
Mathematics Subject Classification ID: 19F27
Mathematics Subject Classification ID: 19D10
Mathematics Subject Classification ID: 19E20
Mathematics Subject Classification ID: 14F20
zbMATH DE Number: 527435
zbMATH Keywords: etale topology
zbMATH Keywords: topological model of ring
zbMATH Keywords: etale cohomology of ring
zbMATH Keywords: algebraic \(K\)-theory
zbMATH Keywords: \(\text{mod } \ell\) model
zbMATH Keywords: affine curve
zbMATH Keywords: local field
zbMATH Keywords: etale \(K\)-theory
zbMATH Keywords: Lichtenbaum-Quillen conjecture
reviewed by: Paul Cherenack
MaRDI profile type: Publication
full work available at URL: 0040-9383(94)90032-9
OpenAlex ID: W1980964327
description: scientific article; zbMATH DE number 527435