The norm map on the Bloch group for quadratic extensions

TL;DR

This paper derives an explicit formula for the norm map on the Bloch group in quadratic extensions, building on Rudenko's proof of homotopy invariance of polylogarithmic complexes.

Contribution

It provides the first explicit formula for the norm map on the Bloch group specifically for quadratic extensions, leveraging recent homotopy invariance results.

Findings

Explicit formula for the norm map in quadratic extensions

Extension of homotopy invariance to norm map properties

Enhanced understanding of polylogarithmic complexes

Abstract

D. Rudenko proved the homotopy invariance of the truncated polylogarithmic complexes. It follows that on these complexes there is the norm map with good proprieties. We apply his result and get the explicit formula for the norm map in the case of quadratic extensions.