2009/07/29 by José Ignacio Burgos Gil, J. I. Burgos Gil, Gil, J. I. Burgos +3
Mathematics · #14C15 #14F43 #14G40 #Advanced Topology and Set Theory #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #math.AG #msc:14C15 #msc:14F43 #msc:14G40
paper · pdf · doi:10.48550/arxiv.0907.5169
arxiv created 2009/07/29 · openalex publication_date 2009/07/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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. The degree zero group agrees 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.