The defect of weak approximation for a reductive group over a global field

TL;DR

This paper investigates the limitations of weak approximation for reductive groups over global fields, linking these limitations to the algebraic fundamental group of the group.

Contribution

It provides a formula to compute the defect of weak approximation using the algebraic fundamental group of the reductive group.

Findings

Explicit computation of the defect of weak approximation.

Connection established between the defect and the algebraic fundamental group.

Enhanced understanding of approximation properties for reductive groups.

Abstract

We compute the defect of weak approximation for a reductive group G over a global field K in terms of the algebraic fundamental group of G.