On Goncharov's regulator and higher arithmetic Chow groups

J. I. Burgos Gil; Elisenda Feliu; Y. Takeda

doi:10.1093/imrn/rnq066

On Goncharov's regulator and higher arithmetic Chow groups

J. I. Burgos Gil, Elisenda Feliu, Y. Takeda

Institut for Matematiske Fag

4 Citationer (Scopus)

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.

Originalsprog	Udefineret/Ukendt
Tidsskrift	International Mathematics Research Notices
Udgave nummer	1
Sider (fra-til)	40-73
Antal sider	34
ISSN	1073-7928
DOI	https://doi.org/10.1093/imrn/rnq066
Status	Udgivet - 1 jan. 2011

Adgang til dokumentet

10.1093/imrn/rnq066

http://imrn.oxfordjournals.org/content/2011/1/40.abstract

Citationsformater

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AU - Feliu, Elisenda

AU - Takeda, Y.

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AB - 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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