An explicit basis for the rational higher Chow groups of abelian number fields

TL;DR

This paper simplifies Beilinson's construction of a basis for the motivic cohomology of cyclotomic fields, extends it to higher Chow cycles, and evaluates the regulator map on these elements.

Contribution

It provides an explicit basis for the rational higher Chow groups of abelian number fields and evaluates the regulator map on these basis elements.

Findings

Explicit basis for higher Chow groups of abelian number fields

Evaluation of the KLM regulator map on basis elements

Simplification of Beilinson's original construction

Abstract

We review and simplify A. Beilinson's construction of a basis for the motivic cohomology of a point over a cyclotomic field, then promote the basis elements to higher Chow cycles and evaluate the KLM regulator map on them.