In this paper, we show that the regulator defined by Goncharov in  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 . 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.
!!!All Science Journal Classification (ASJC) codes
- 数学 (全般)