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arXiv · 0904.2563

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

T. Chinburg·G. Pappas·M. Taylor
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Abstract

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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T. Chinburg, G. Pappas, M. Taylor. 2009-04-16. K_1 of a p-adic group ring I. The determinantal image. https://arxiv.org/abs/0904.2563

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