On the topological cyclic homology of the integers

Abstract

This article provides a computation of the mod p homotopy groups of the fixed points of the Topological Hochschild Homology of the ring of integers under the action of any finite subgroup of the cirle group whose order is a power of an odd prime p . This leads to a computation of the Topological Cyclic Homology groups of the ring of integers, and determines also the p -adic completion of the algebraic K -theory of the p -adic integers.