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On the third homology of SL_2 and weak homotopy invariance
Author(s)
Date Issued
2015-11-12
Date Available
2016-12-12T11:10:44Z
Abstract
The goal of the paper is to achieve - in the special case of the linear group SL2 - some understanding of the relation between group homology and its A1-invariant replacement. We discuss some of the general properties of the A1-invariant group homology, such as stabilization sequences and Grothendieck-Witt module structures. Together with very precise knowledge about refined Bloch groups, these methods allow us to deduce that in general there is a rather large difference between group homology and its A1 -invariant version. In other words, weak homotopy invariance fails for SL2 over many families of non-algebraically closed fields.
Type of Material
Journal Article
Publisher
American Mathematical Society
Journal
Transactions of the American Mathematical Society
Volume
367
Issue
10
Start Page
7481
End Page
7513
Copyright (Published Version)
2014 American Mathematical Society
Language
English
Status of Item
Peer reviewed
ISSN
0002-9947
This item is made available under a Creative Commons License
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