nLab
Tate spectrum

Contents

Context

Stable Homotopy theory

Representation theory

Contents

Idea

For ∞-actions of finite groups GG on objects EE in stable (∞,1)-categories, then the homotopy cofiber X tGX^{t G} of the norm map is called the Tate construction, sitting in a homotopy fiber sequence

X GnormX GX tG. X_G \stackrel{norm}{\longrightarrow} X^G \longrightarrow X^{t G} \,.

(e.g Lurie, def. 6.1.6.24)

Depending on which edition you have, chapter 6 may be chapter 7.

For the stable (∞,1)-category of spectra this is accordingly called the Tate spectrum.

Examples

References

The general abstract discussion is due to

Review with an eye towards topological cyclic homology is in

Last revised on July 25, 2017 at 11:57:16. See the history of this page for a list of all contributions to it.