Milnor K-theory of complete discrete valuation rings with finite residue fields

2015/09/30 by Christian Dahlhausen
Mathematics · #Algebraic Geometry and Number Theory #Combinatorics #Conjecture #Crystallography #Discrete mathematics #Discrete valuation #Discrete valuation ring #Field (mathematics) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Isomorphism (crystallography) #Mathematics #Pure mathematics #Quotient #Residue (chemistry) #Residue field #Valuation (finance) #math.KT

paper · pdf · doi:10.1016/j.jpaa.2017.07.002

18 pages. An edited version will appear in J. Pure Appl. Algebra (2017)

openalex publication_date 2017/07/15 · arxiv created 2017/07/19 · arxiv updated 2017/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Consider a complete discrete valuation ring O with quotient field F and finite residue field. Then the inclusion map O \hookrightarrow F induces a map K^M_*O → K^M_*F on improved Milnor K-theory. We show that this map is an isomorphism in degrees bigger or equal to 3. This implies the Gersten conjecture for improved Milnor K-theory. This result is new in the p-adic case.

Citations

• AlgebraicK-theory and quadratic forms