### On the relative and bi-relative K-theory of rings of finite
characteristic

We prove that the relative *K*-groups associated with a
nilpotent extension of **Z**/p^{N}**Z**-algebras and the
bi-relative *K*-groups associated with a Milnor square of
**Z**/p^{N}**Z**-algebras are p-primary torsion groups
of bounded exponent. We also show that the cyclotomic trace map extends from
Quillen *K*-theory to Bass completed non-connective
*K*-theory.

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