On Goncharov's regulator and higher arithmetic Chow groups

Details On Goncharov's regulator and higher arithmetic Chow groups On Goncharov's regulator and higher arithmetic Chow groups

2009-09-29

arxiv.org/abs/0909.5296v1

Mathematics

Algebraic Geometry

Scientific paper

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 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 and Feliu.

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