K₁ of a p-adic group ring I. The determinantal image

2009/04/16 by Chinburg, T., Pappas, G., Taylor, M.
#FOS: Mathematics #K-Theory and Homology (math.KT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.0904.2563

Abstract

We study the K-group K₁ of the group ring of a finite group over a coefficient ring which is p-adically complete and admits a lift of Frobenius. In this paper, we consider the image of K₁ under the determinant map; the central tool is the group logarithm which we can define using the Frobenius lift. Using this we prove a fixed point theorem for the determinantal image of K₁.

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