The Brauer-Manin obstruction for sections of the fundamental group

TL;DR

This paper proves Grothendieck's section conjecture for a specific algebraic curve and introduces a new obstruction concept for sections of the fundamental group, advancing understanding in arithmetic geometry.

Contribution

It establishes the section conjecture for an open subset of the Reichardt-Lind curve and defines a Brauer-Manin obstruction for fundamental group sections, a novel theoretical development.

Findings

Grothendieck's section conjecture proven for a specific curve

Introduction of a Brauer-Manin obstruction for fundamental group sections

New theoretical framework for arithmetic obstructions

Abstract

We establish Grothendieck's section conjecture for an open subset of the Reichardt-Lind curve, and introduce the notion of a Brauer-Manin obstruction for sections of the fundamental group extension.