A local-global principle for torsors under geometric prosolvable fundamental groups

TL;DR

This paper establishes a local-global principle for torsors under the prosolvable geometric fundamental group of hyperbolic curves over number fields, advancing understanding in arithmetic geometry.

Contribution

It introduces a new local-global principle specifically for torsors under prosolvable fundamental groups of hyperbolic curves over number fields.

Findings

Proves a local-global principle for torsors under prosolvable fundamental groups.

Applies to hyperbolic curves over number fields.

Enhances the understanding of arithmetic properties of fundamental groups.

Abstract

We prove a local-global principle for torsors under the prosolvable geometric fundamental group of a hyperbolic curve over a number field.