K₁ of a p-adic group ring II. The determinantal kernel SK₁

2013/03/21 by Ted Chinburg, Chinburg, T., G. Pappas +3
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #K-Theory and Homology (math.KT) #Number Theory (math.NT) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1303.5337

openalex publication_date 2013/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe the group SK₁(R[G]) for group rings R[G] where G is an arbitrary finite group and where the coefficient ring R is a p-adically complete Noetherian integral domain of characteristic zero which admits a lift of Frobenius and which also satisfies a number of further mild conditions. Our results extend previous work of R. Oliver who obtained such results for the valuation rings of finite extensions of the p-adic field.

Cited by

• Higher adeles and non-abelian Riemann-Roch

Related

• K₁ of a p-adic group ring I. The determinantal image
• Group Determinants and Invariant Rings
• Slope filtrations for relative Frobenius
• Finitude pour les representations lisses de groupes p-adiques
• Galois descent of determinants in the ramified case