# Obstructions to weak approximation for reductive groups over $p$-adic function fields

## TL;DR

This paper develops duality theorems for reductive groups over p-adic function fields and uses them to identify obstructions to weak approximation, linking these to unramified Galois cohomology.

## Contribution

It introduces new duality results for complexes associated with reductive groups over p-adic function fields and connects obstructions to weak approximation with Galois cohomology.

## Key findings

- Established arithmetic duality theorems for reductive groups over p-adic function fields.
- Identified obstructions to weak approximation for certain reductive groups.
- Linked these obstructions to unramified Galois cohomology groups.

## Abstract

We establish arithmetic duality theorems for short complexes associated to reductive groups over $p$-adic function fields. Using dualities, we deduce obstructions to weak approximation for certain reductive groups (especially quasi-split ones) and relate this obstruction to an unramified Galois cohomology group.