Adelic double cosets over semi-global fields

TL;DR

This paper explores adelic double coset spaces over semi-global fields, connecting them to local-global principles and torsors, and provides explicit examples to illustrate these relationships.

Contribution

It establishes a framework for adelic double coset spaces over semi-global fields and relates them to classical global field concepts, with explicit examples.

Findings

Established adelic double coset spaces over semi-global fields

Connected these spaces to local-global principles and torsors

Provided explicit examples illustrating the theory

Abstract

Double coset spaces of adelic points on linear algebraic groups arise in the study of global fields; e.g., concerning local-global principles and torsors. A different type of double coset space plays a role in the study of semi-global fields such as p-adic function fields. This paper relates the two, by establishing adelic double coset spaces over semi-global fields; relating them to local-global principles and torsors; and providing explicit examples.