On Goncharov's regulator and higher arithmetic Chow groups
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On Goncharov's regulator and higher arithmetic Chow groups. / Gil, J. I. Burgos; Feliu, Elisenda; Takeda, Y.
In: International Mathematics Research Notices, No. 1, 2011, p. 40-73.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - On Goncharov's regulator and higher arithmetic Chow groups
AU - Gil, J. I. Burgos
AU - Feliu, Elisenda
AU - Takeda, Y.
PY - 2011
Y1 - 2011
N2 - 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 Gil 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 Gil and Feliu.
AB - 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 Gil 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 Gil and Feliu.
U2 - 10.1093/imrn/rnq066
DO - 10.1093/imrn/rnq066
M3 - Journal article
SP - 40
EP - 73
JO - International Mathematics Research Notices
JF - International Mathematics Research Notices
SN - 1073-7928
IS - 1
ER -
ID: 40285376