K_1 of a p-adic group ring I. The determinantal image

Details K_1 of a p-adic group ring I. The determinantal image K_1 of a p-adic group ring I. The determinantal image

2009-04-16

arxiv.org/abs/0904.2563v1

Mathematics

K-Theory and Homology

39 pp

Scientific paper

We study the K-group K_1 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 K_1 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 K_1.

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