### 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 Nrd_{D/K}
: *K*_{j}(*D*, **Z**_{l}) → *K*_{j}(*K*, **Z**_{l})
such that *d* · Nrd_{D/K}
= *N*_{D/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>