$p$-adic Cocycles and their Regulator Maps

TL;DR

This paper presents a power series formula for the $p$-adic regulator on higher algebraic K-groups of number fields, facilitating computational and modular reduction applications, and explores related conjectural questions.

Contribution

It introduces a computationally friendly power series formula for $p$-adic regulators and discusses higher K-theoretic analogues of Gross and Serre conjectures.

Findings

Power series formula suitable for computer calculations

Reduction modulo powers of $p$ enabled

Discussion of higher K-theoretic regulator conjectures

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.