# nLab Dennis trace

### Context

#### Higher algebra

higher algebra

universal algebra

# Contents

## Idea

The Dennis trace is a natural morphism from algebraic K-theory of rings to Hochschild homology

$K(-) \longrightarrow THH(-) \,.$

While various versions of Chern character are maps from K-theory to some (co)homology of a space, algebra, scheme, the Dennis trace map underlies this phenomenon at the more fundamental level of K-theory space.

The Dennis trace lifts to to ring spectra and as such factors through the map $TC(-) \longrightarrow THH(-)$ ]] from topological cyclic homology, this lift is called the cyclotomic trace.

## Literature

Revised on November 6, 2015 16:11:42 by Urs Schreiber (178.197.231.215)