Higher arithmetic Chow groups

J. I. Burgos Gil; Elisenda Feliu

Higher arithmetic Chow groups

Department of Mathematical Sciences

3 Citations (Scopus)

Abstract

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.

Original language	English
Journal	Commentarii Mathematici Helvetici
Volume	87
Issue number	3
Pages (from-to)	521-587
ISSN	0010-2571
Publication status	Published - 2012

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title = "Higher arithmetic Chow groups",

abstract = "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 Soul{\'e}, 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.",

author = "Gil, {J. I. Burgos} and Elisenda Feliu",

year = "2012",

language = "English",

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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

SN - 0010-2571

VL - 87

SP - 521

EP - 587

JO - Commentarii Mathematici Helvetici

JF - Commentarii Mathematici Helvetici

IS - 3

ER -

Higher arithmetic Chow groups

Abstract

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