JournalscmhVol. 87, No. 3pp. 521–587

Higher arithmetic Chow groups

  • José Ignacio Burgos Gil

    Madrid, Spain
  • Elisenda Feliu

    University of Copenhagen, Denmark
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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.

Cite this article

José Ignacio Burgos Gil, Elisenda Feliu, Higher arithmetic Chow groups. Comment. Math. Helv. 87 (2012), no. 3, pp. 521–587

DOI 10.4171/CMH/262