Milnor-Witt K-groups of local rings

2015/01/29 by Stefan Gille, Stephen Scully, Gille, Stefan +3
Mathematics · #11E08 #11E81 #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)

paper · pdf · doi:10.48550/arxiv.1501.07631

openalex publication_date 2015/01/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 fields.

Related

• Milnor-Witt K-theory and Witt K-theory of a field
• Periodicity of hermitian K-theory and Milnor's K-groups
• The Witt Ring of a Curve with Good Reduction over a Non-dyadic Local Field
• Invitation to higher local fields, Part I, section 6: Topological Milnor K-groups of higher local fields
• Invitation to higher local fields, Part I, section 2: p-primary part of the Milnor K-groups and Galois cohomology of fields of characteristic p