Milnor-Witt K-groups of local rings

Stefan Gille; Stephen Scully; Changlong Zhong

doi:10.1016/j.aim.2015.09.014

Milnor-Witt K-groups of local rings

Stefan Gille
, Stephen Scully
, Changlong Zhong

Mathematics and Statistics

University at Albany

University of Alberta

Research output: Contribution to journal › Article › peer-review

18 Scopus citations

Abstract

We introduce Milnor-Witt K-groups of local rings and show that the nth Milnor-Witt K-group of a local ring R which contains an infinite field of characteristic not 2 is the pull-back of the nth power of the fundamental ideal in the Witt ring of R and the nth Milnor K-group of R over the nth Milnor K-group of R modulo 2. This generalizes the work of Morel-Hopkins on Milnor-Witt K-groups of a field.

Original language	English
Pages (from-to)	729-753
Number of pages	25
Journal	Advances in Mathematics
Volume	286
DOIs	https://doi.org/10.1016/j.aim.2015.09.014
State	Published - Jan 2 2016

Keywords

Milnor-Witt K-groups
Quadratic forms
Regular local rings
Witt groups

Access to Document

10.1016/j.aim.2015.09.014

Cite this

@article{5ecfdb806b79454bb847d3c4051d14e3,

title = "Milnor-Witt K-groups of local rings",

abstract = "We introduce Milnor-Witt K-groups of local rings and show that the nth Milnor-Witt K-group of a local ring R which contains an infinite field of characteristic not 2 is the pull-back of the nth power of the fundamental ideal in the Witt ring of R and the nth Milnor K-group of R over the nth Milnor K-group of R modulo 2. This generalizes the work of Morel-Hopkins on Milnor-Witt K-groups of a field.",

keywords = "Milnor-Witt K-groups, Quadratic forms, Regular local rings, Witt groups",

author = "Stefan Gille and Stephen Scully and Changlong Zhong",

note = "Publisher Copyright: {\textcopyright} 2015 Elsevier Inc.",

year = "2016",

month = jan,

day = "2",

doi = "10.1016/j.aim.2015.09.014",

language = "English",

volume = "286",

pages = "729--753",

journal = "Advances in Mathematics",

issn = "0001-8708",

publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - Milnor-Witt K-groups of local rings

AU - Gille, Stefan

AU - Scully, Stephen

AU - Zhong, Changlong

PY - 2016/1/2

Y1 - 2016/1/2

N2 - We introduce Milnor-Witt K-groups of local rings and show that the nth Milnor-Witt K-group of a local ring R which contains an infinite field of characteristic not 2 is the pull-back of the nth power of the fundamental ideal in the Witt ring of R and the nth Milnor K-group of R over the nth Milnor K-group of R modulo 2. This generalizes the work of Morel-Hopkins on Milnor-Witt K-groups of a field.

AB - We introduce Milnor-Witt K-groups of local rings and show that the nth Milnor-Witt K-group of a local ring R which contains an infinite field of characteristic not 2 is the pull-back of the nth power of the fundamental ideal in the Witt ring of R and the nth Milnor K-group of R over the nth Milnor K-group of R modulo 2. This generalizes the work of Morel-Hopkins on Milnor-Witt K-groups of a field.

KW - Milnor-Witt K-groups

KW - Quadratic forms

KW - Regular local rings

KW - Witt groups

UR - https://www.scopus.com/pages/publications/84943770411

U2 - 10.1016/j.aim.2015.09.014

DO - 10.1016/j.aim.2015.09.014

M3 - Article

SN - 0001-8708

VL - 286

SP - 729

EP - 753

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

Milnor-Witt K-groups of local rings

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this