Homology stability for the special linear group of a field and Milnor-Witt K-theory

Files in This Item:
File Description SizeFormat 
MilnorWitt-Documenta.pdf393.04 kBAdobe PDFDownload
Title: Homology stability for the special linear group of a field and Milnor-Witt K-theory
Authors: Hutchinson, Kevin
Tao, Liqun
Permanent link: http://hdl.handle.net/10197/6586
Date: Jun-2010
Abstract: Let F be a field of characteristic zero and let ft,n be the stabilization homomorphism Hn(SLt(F), Z) → Hn(SLt+1(F), Z). We prove the following results: For all n, ft,n is an isomorphism if t ≥ n + 1 and is surjective for t = n, confirming a conjecture of C-H. Sah. fn,n is an isomorphism when n is odd and when n is even the kernel is isomorphic to I n+1(F), the (n + 1)st power of the fundamental ideal of the Witt Ring of F. When n is even the cokernel of fn−1,n is isomorphic to KMW n (F), the nth Milnor-Witt K-theory group of F. When n is odd, the cokernel of fn−1,n is isomorphic to 2KM n (F), where KM n (F) is the nth Milnor K-group of F.
Type of material: Journal Article
Publisher: Universität Bielefeld
Journal: Documenta Mathematica
Volume: Extra volume: Andrea A. Suslin's Sixieth Birthday
Start page: 267
End page: 315
Keywords: K-theorySpecial linear groupGroup homology
Other versions: https://www.math.uni-bielefeld.de/documenta/vol-suslin/hutchinson_tao.html
Language: en
Status of Item: Peer reviewed
Appears in Collections:Mathematics and Statistics Research Collection

Show full item record

Page view(s) 50

22
checked on May 25, 2018

Download(s) 50

14
checked on May 25, 2018

Google ScholarTM

Check


This item is available under the Attribution-NonCommercial-NoDerivs 3.0 Ireland. No item may be reproduced for commercial purposes. For other possible restrictions on use please refer to the publisher's URL where this is made available, or to notes contained in the item itself. Other terms may apply.