Contou-Carrere symbol via iterated integrals and its reciprocity law

TL;DR

This paper introduces a novel definition of the Contou-Carrere symbol using Chen iterated integrals and establishes its reciprocity law, providing a new perspective on this mathematical concept.

Contribution

It offers a new formulation of the Contou-Carrere symbol through iterated integrals and proves its reciprocity law, advancing the theoretical understanding of this symbol.

Findings

New definition of Contou-Carrere symbol via iterated integrals

Proof of the reciprocity law for the new symbol

Enhanced theoretical framework for the symbol's properties

Abstract

This paper gives a new definition of the Contou-Carrere symbol in terms of an exponential of a Chen iterated integral and proves the corresponding reciprocity law.