Integral Regulators for Higher Chow Complexes

Building on Kerr, Lewis and Müller–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 Kerr–Lewis–Müller-Stach, Petras, and Kerr–Yang.