$p$-adic Cocycles and their Regulator Maps

Abstract

We derive a power series formula for the $p$-adic regulator on the higher dimensional algebraic K-groups of number fields. This formula is designed to be well suited to computer calculations and to reduction modulo powers of $p$. In addition we describe a series of regulator questions concerning higher dimensional K-theoretic analogues of conjectures of Gross and Serre.