Karoubi’s relative Chern character and Beilinson’s regulator

Abstract

We construct a variant of Karoubi's relative Chem character for smooth varieties over C and prove a comparison result with Beilinson's regulator with values in Deligne-Beilinson cohomology. As a corollary we obtain a new proof of Burgos' Theorem that for number fields Borel's regulator is twice Beilinson's regulator.