Chow dilogarithm and strong Suslin reciprocity law

TL;DR

This paper proves Goncharov's conjecture on the strong Suslin reciprocity law by constructing a norm map, and relates the Chow dilogarithm to the Bloch-Wigner dilogarithm, introducing a new reciprocity law for algebraic surfaces.

Contribution

It introduces a novel construction of the norm map on lifted reciprocity maps and proves a conjecture linking reciprocity laws and dilogarithms.

Findings

Proof of Goncharov's conjecture on strong Suslin reciprocity law

Expression of Chow dilogarithm via Bloch-Wigner dilogarithm

New reciprocity law for rational functions on algebraic surfaces

Abstract

We prove a conjecture of A. Goncharov concerning strong Suslin reciprocity law. The main idea of the proof is the construction of the norm map on so-called lifted reciprocity maps. This construction is similar to the construction of the norm map on Milnor $K$-theory. As an application, we express Chow dilogarithm in terms of Bloch-Wigner dilogarithm. Also, we obtain a new reciprocity law for four rational functions on an arbitrary algebraic surface with values in the pre-Bloch group.