### Syntomic regulators and p-adic integration II K_2 of curves, by Amnon Besser

Coleman and de Shalit constructed, using Coleman's theory of *p*-adic
integration, a *p*-adic ``regulator'' on the K_{2} of curves
over C_{p}. They showed that in the case where the curve is an
elliptic curve with complex multiplication E defined over Q there is a
relation between the regulator and a special value of the *p*-adic
L-function of E, which is a *p*-adic analogue of a formula of Bloch and
Beilinson in the complex case. We show that in the case of good reduction
their regulator is equivalent to the syntomic regulator of Gros and
Niziol. This last regulator can be defined in complete generality for any
K-group. Our result, together with the result of Coleman and de Shalit,
therefore gives an instance of a ``*p*-adic Beilinson conjecture'',
whose precise nature is still unknown.

Later versions of this work as well as other papers of mine are available
here
and in the future will be available
here.

Amnon Besser <Amnon.Besser@durham.ac.uk>