Integral Regulators for Higher Chow Complexes

TL;DR

This paper establishes the existence of an integral regulator for higher Chow complexes, providing explicit formulas and strengthening the theoretical foundation for torsion phenomena in higher cycle groups.

Contribution

It introduces an integral regulator for higher Chow complexes, extending prior rational regulator work to integral settings with explicit expressions.

Findings

Proves the existence of an integral regulator for higher Chow complexes.

Provides explicit formulas for the integral regulator.

Supports earlier conjectures on torsion in higher cycle groups.

Abstract

Building on Kerr, Lewis and Mueller-Stach's work on the rational regulator, we prove the existence of an integral regulator on higher Chow complexes and give an explicit expression. This puts firm ground under some earlier results and speculations on the torsion in higher cycle groups by K-L-M, Petras, and Kerr-Yang.