Higher arithmetic Chow groups

J. I. Burgos Gil, Elisenda Feliu

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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 languageEnglish
JournalCommentarii Mathematici Helvetici
Volume87
Issue number3
Pages (from-to)521-587
ISSN0010-2571
Publication statusPublished - 2012

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