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"
: 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