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- Title
Higher arithmetic Chow groups.
- Authors
Burgos Gil, José Ignacio; Feliu, Elisenda
- 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.
- Subjects
MATHEMATICAL functions; HOMOLOGY theory; MATHEMATICAL analysis; MATHEMATICS theorems; ALGEBRA; ARAKELOV theory; CONTRAVARIANT &; covariant vectors
- Publication
Commentarii Mathematici Helvetici, 2012, Vol 87, Issue 3, p521
- ISSN
0010-2571
- Publication type
Article
- DOI
10.4171/CMH/262