Galois descent of determinants in the ramified case

2010/10/30 by Victor Snaith, Snaith, Victor
Mathematics · #11S23 #19B28 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #FOS: Mathematics #K-Theory and Homology (math.KT) #Number Theory (math.NT) #math.KT #math.NT #msc:11S23 #msc:19B28

paper · pdf · doi:10.48550/arxiv.1011.0080

12 pages

arxiv created 2010/10/30 · openalex publication_date 2010/10/30 · arxiv updated 2010/11/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the local, unramified case the determinantal functions associated to the group-ring of a finite group satisfy Galois descent. This note examines the obstructions to Galois determinantal descent in the ramified case.

Related

• Ramification in the Inverse Galois Problem
• K₁ of a p-adic group ring I. The determinantal image
• K₁ of a p-adic group ring II. The determinantal kernel SK₁
• Galois extensions ramified only at one prime
• Generalization of Frobenius' theorem for group determinants