The cyclotomic trace for symmetric ring spectra

TL;DR

This paper introduces a straightforward and explicit construction of the cyclotomic trace linking algebraic K-theory and topological cyclic homology, integrating Goodwillie's global trace concept.

Contribution

It provides a simplified and explicit method for constructing the cyclotomic trace, enhancing understanding and potential applications in algebraic K-theory and topological cyclic homology.

Findings

Explicit construction of the cyclotomic trace

Incorporation of Goodwillie's global trace idea

Simplification of previous complex methods

Abstract

The purpose of this paper is to present a simple and explicit construction of the Bokstedt-Hsiang-Madsen cyclotomic trace relating algebraic K-theory and topological cyclic homology. Our construction also incorporates Goodwillie's idea of a global cyclotomic trace.