On Goncharov's regulator and higher arithmetic Chow groups

In this paper, we show that the regulator defined by Goncharov from higher algebraic Chow groups to Deligne–Beilinson cohomology agrees with Beilinson’s regulator. We give a direct comparison of Goncharov’s regulator to the construction given by Burgos Gil and Feliu. As a consequence, we show that the higher arithmetic Chow groups defined by Goncharov agree, for all projective arithmetic varieties over an arithmetic field, with the ones defined by Burgos Gil and Feliu.