On the K-theory of division algebras over local fields

Let K be a complete discrete valuation field with finite residue field of charactersitic p, and let D be a central division algebra over K of finite index d. Thirty years ago, Suslin and Yufryakov showed that for all prime numbers l different from p and integers j ≥ 1, there exists a canonical "reduced norm" isomorphism NrdD/K : Kj(D, Zl) → Kj(K, Zl) such that d · NrdD/K = ND/K. The purpose of this paper is to prove the analogous statement for the p-adic K-groups. The published paper is available here.

Lars Hesselholt <larsh@math.nagoya-u.ac.jp>