The algebraic Brauer group of a reductive group over a nonarchimedean local field

TL;DR

This paper demonstrates that for reductive groups over nonarchimedean local fields, the algebraic Brauer group pairing fully characterizes all continuous homomorphisms from the group to , extending previous results.

Contribution

It generalizes existing results by showing the algebraic Brauer group pairing captures all continuous homomorphisms for reductive groups over nonarchimedean local fields.

Findings

The pairing from the algebraic Brauer group characterizes all continuous homomorphisms.

Extension of previous results by Loughran and others.

Provides a comprehensive understanding of the algebraic Brauer group in this context.

Abstract

We show that for nonarchimedean local fields $F$, the pairing from the algebraic part of the Brauer group of a reductive group $G$ characterizes all continuous homomorphisms from $G(F)$ into $\mathbb{Q}/\mathbb{Z}$. This generalizes results of Loughran and Loughran-Tanimoto-Takloo-Bighash.