Admissibility of groups over function fields of p-adic curves

2012/01/09 by B. Surendranath Reddy, Reddy, B. Surendranath, V. Suresh +1
Mathematics · #11R52 #12E15 #12E30 #12F12 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT) #Rings and Algebras (math.RA) #math.NT #math.RA #msc:11R52 #msc:12E15 #msc:12E30 #msc:12F12

paper · pdf · doi:10.48550/arxiv.1201.1938

arxiv created 2012/01/09 · openalex publication_date 2012/01/09 · arxiv updated 2012/01/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let K be a field and G a finite group. The question of 'admissibility' of G over K was originally posed by Schacher, who gave partial results in the case K = Q. In this paper, we give necessary conditions for admissibility of a finite group G over function fields of curves over complete discretely valued fields. Using this criterion, we give an example of a finite group which is not admissible over Qp(t). We also prove a certain Hasse principle for division algebras over such fields.

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