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Abstract: We give a new construction of higher arithmetic Chow groups forquasi-projective arithmetic varieties over a field. Our definition agrees withthe higher arithmetic Chow groups defined by Goncharov for projectivearithmetic varieties over a field. These groups are the analogue, in theArakelov context, of the higher algebraic Chow groups defined by Bloch. Thedegree zero group agrees with the arithmetic Chow groups of Burgos. Our newconstruction is shown to be a contravariant functor and is endowed with aproduct structure, which is commutative and associative.

Author: J. I. Burgos Gil, E. Feliu

Source: https://arxiv.org/


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