nLab Tate spectrum

Contents

Context

Representation theory

representation theory

geometric representation theory

Contents

Idea

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

$X_G \stackrel{norm}{\longrightarrow} X^G \longrightarrow X^{t G} \,.$

(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.

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.