2009/06/08 by Elisenda Feliu, Feliu, Elisenda
Mathematics · #14G40 #19E08 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #math.AG #math.KT #msc:14G40 #msc:19E08
paper · pdf · doi:10.48550/arxiv.0906.1488
arxiv created 2009/06/08 · openalex publication_date 2009/06/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct Adams operations on the rational higher arithmetic K-groups of a proper arithmetic variety. The definition applies to the higher arithmetic K-groups given by Takeda as well as to the groups suggested by Deligne and Soule, by means of the homotopy groups of the homotopy fiber of the regulator map. They are compatible with the Adams operations on algebraic K-theory. The definition relies on the chain morphism representing Adams operations in higher algebraic K-theory given previously by the author. In this paper it is shown that a slight modification of this chain morphism commutes strictly with the representative of the Beilinson regulator given by Burgos and Wang.