Syntomic regulators andp-adic integration II:K 2 of curves

Abstract

We show that the ad hoc regulator of Coleman and de Shalit for elements of K2 of curves evaluated on a holomorphic differential is the same as the syntomic regulator of the same elements cup produced with the same differential. Combined with the results of Coleman and de Shalit this gives a relation between syntomic regulators and special values of p-adic L-functions. The main technical innovation is the notion of a local index-a kind of generalized residue.