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

2019/04/10 by Yisheng Tian, Tian, Yisheng · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1904.05225

openalex publication_date 2019/04/10 · openalex created_date 2019/04/25 · openalex updated_date 2026/07/28

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.

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