Higher arithmetic Chern character

TL;DR

This paper introduces a higher arithmetic Chern character map linking higher arithmetic K-groups to higher arithmetic Chow groups, extending previous work and aligning with Beilinson's regulator in Arakelov geometry.

Contribution

It constructs a new higher arithmetic Chern character map that generalizes existing theories and demonstrates its compatibility with pull-backs and product structures.

Findings

The map extends the arithmetic Chern character to higher K-theory.

It is compatible with pull-back maps.

It respects the product structure in the relevant theories.

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 Soul\'{e}, 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.