Higher arithmetic Chow groups
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Higher arithmetic Chow groups. / Gil, J. I. Burgos; Feliu, Elisenda.
I: Commentarii Mathematici Helvetici, Bind 87, Nr. 3, 2012, s. 521-587.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Higher arithmetic Chow groups
AU - Gil, J. I. Burgos
AU - Feliu, Elisenda
PY - 2012
Y1 - 2012
N2 - We give a new construction of higher arithmetic Chow groups for quasi-projective arithmetic varieties over a field. Our definition agrees with the higher arithmetic Chow groups defined by Goncharov for projective arithmetic varieties over a field. These groups are the analogue, in the Arakelov context, of the higher algebraic Chow groups defined by Bloch. For projective varieties the degree zero group agrees with the arithmetic Chow groups defined by Gillet and Soulé, and in general with the arithmetic Chow groups of Burgos. Our new construction is shown to be a contravariant functor and is endowed with a product structure, which is commutative and associative.
AB - We give a new construction of higher arithmetic Chow groups for quasi-projective arithmetic varieties over a field. Our definition agrees with the higher arithmetic Chow groups defined by Goncharov for projective arithmetic varieties over a field. These groups are the analogue, in the Arakelov context, of the higher algebraic Chow groups defined by Bloch. For projective varieties the degree zero group agrees with the arithmetic Chow groups defined by Gillet and Soulé, and in general with the arithmetic Chow groups of Burgos. Our new construction is shown to be a contravariant functor and is endowed with a product structure, which is commutative and associative.
M3 - Journal article
VL - 87
SP - 521
EP - 587
JO - Commentarii Mathematici Helvetici
JF - Commentarii Mathematici Helvetici
SN - 0010-2571
IS - 3
ER -
ID: 40285632