Topological Cyclic Homology of Local Fields

Abstract

We introduce a new approach to determining the structure of topological cyclic homology by means of a descent spectral sequence. We carry out the computation for a p-adic local field with Fp-coefficients, including the case p=2 which was only covered by motivic methods except in the totally unramified case.

Refereed version; the constant term of the Eisenstein polynomial is obtained directly, and the original section 9 is removed; the original Theorem 3.24 is moved to the new appendix A, and the detailed proof is given there