nLab cyclotomic trace

Context

Higher algebra

higher algebra

universal algebra

Contents

Idea

Given a ring $R$, then there is a natural morphism of spectra

$\array{ && \mathbf{TC}(R) \\ & \nearrow & \downarrow \\ \mathbf{K}(R) &\longrightarrow& \mathbf{THH}(R) }$

from the algebraic K-theory spectrum to the topological Hochschild homology spectrum and factoring through the topological cyclic homology spectrum (a cyclotomic spectrum) called the cyclotomic trace which much like a Chern character map for algebraic K-theory.

This is a refinement to spectra of the Dennis trace.

References

For a very brief, very elementary introduction, see

For more see the references at topological Hochschild homology.