Coleman and de Shalit constructed, using Coleman's theory of p-adic
integration, a p-adic ``regulator'' on the K2 of curves
over Cp. 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
and in the future will be available
Later versions of this work as well as other papers of mine are available here and in the future will be available here.