### The syntomic regulator for K-theory of fields, by Amnon Besser and Rob de Jeu

We define complexes analogous to Goncharov's complexes for the
K-theory of discrete valuation rings of characteristic zero.
Under suitable assumptions in K-theory, there is a map from
the cohomology of those complexes to the K-theory of the
ring. In case the ring is the localization of the ring of integers
in a number field, there are no assumptions necessary. We compute
the composition of our map to the K-theory with the syntomic
regulator. The result can be described in terms of a *p*-adic
polylogarithm. Finally, we apply our theory in order to compute
the regulator to syntomic cohomology on Beilinson's cyclotomic elements.
The result is again given by the *p*-adic polylogarithm.
This last result is related to one by Somekawa and generalizes
work by Gros.

Amnon Besser <bessera@math.bgu.ac.il>

Rob de Jeu <Rob.de-Jeu@durham.ac.uk>