Higher arithmetic Chern character

2012/06/11 by Takeda, Yuichiro
#14G40 #19E15 #Algebraic Geometry (math.AG) #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.1206.2100

Abstract

A map from the higher arithmetic K-group defined by the author to the higher arithmetic Chow group constructed by Burgos and Feliu is given. It is a higher extension of the arithmetic Chern character established by Gillet and Soulé, and it can also be regarded as an analogue of Beilinson's regulator in Arakelov geometry. It is shown that this map is compatible with the pull-back map and the product structure.

Related

• The Relative Chern Character and Regulators
• Explicit Chern Cycles in BGL and KV-theory
• A universal characterization of the Chern character maps
• On Goncharov's regulator and higher arithmetic Chow groups
• Notes on the Chern-character