On Goncharov's regulator and higher arithmetic chow groups

José Ignacio Burgos Gil, Elisenda Feliu, Yuichiro Takeda

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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.

Original languageEnglish
Pages (from-to)40-73
Number of pages34
JournalInternational Mathematics Research Notices
Volume2011
Issue number1
DOIs
Publication statusPublished - Jan 5 2011

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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