TY - JOUR
T1 - On Goncharov's regulator and higher arithmetic chow groups
AU - Gil, José Ignacio Burgos
AU - Feliu, Elisenda
AU - Takeda, Yuichiro
N1 - Funding Information:
This work was partially supported by the projects MTM2006-14234-C02-01 and MTM2009-14163-C02-01 from the Spanish Ministry of Ciencia e Innovación and by the Japan Society for the Promotion of Science (JSPS) Grant-in-Aid for Scientific Research (No. 17340009).
PY - 2011/1/1
Y1 - 2011/1/1
N2 - 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.
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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U2 - 10.1093/imrn/rnq066
DO - 10.1093/imrn/rnq066
M3 - Article
AN - SCOPUS:78650721858
SN - 1073-7928
VL - 2011
SP - 40
EP - 73
JO - International Mathematics Research Notices
JF - International Mathematics Research Notices
IS - 1
ER -