Abstract
In this paper, we show that the regulator defined by Goncharov in [10] 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 in [5]. 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.
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