Topological Cyclic Homology of Local Fields

TL;DR

This paper develops a descent spectral sequence approach to compute topological cyclic homology of local fields, successfully including the challenging case p=2, and broadening the understanding of these structures.

Contribution

It introduces a new spectral sequence method for calculating topological cyclic homology of local fields, covering cases previously inaccessible by motivic methods.

Findings

Computed topological cyclic homology for p-adic local fields with Fp-coefficients.

Included the case p=2, previously only handled by motivic methods in special cases.

Demonstrated the effectiveness of the descent spectral sequence approach.

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.