Journal of K-theory: K-theory and its Applications to Algebra, Geometry, and Topology

Table of Contents - June 2012 - Volume 9, Issue 03  

Research Article

Continuity of the norm map on Milnor K-theory

Matthew Morrowa1

a1 University of Chicago, 5734 S. University Ave., Chicago, IL, 60637, USA mmorrow@math.uchicago.edu http://math.uchicago.edu/~mmorrow/

Abstract

The norm map on the Milnor K-groups of a finite extension of complete, discrete valuation fields is continuous with respect to the unit group filtrations. The only proof in the literature, due to K. Kato, uses semi-global methods. Here we present an elementary algebraic proof.

(Received February 21 2011)

Key Words

  • Milnor K-theory;
  • norm map;
  • higher local class field theory