Chromatic Smith theory

Let X be a finite complex equipped with an action of a finite group G. Classical Smith theory studies the relationship between the mod p homology of X and the mod p homology of the fixed point space X^G. In this talk I will describe a variant of this theory where mod p homology is replaced by other generalized homology theories. In particular I will discuss a relationship between the chromatic types of X and  X^G, and how this is related to chromatic blueshift of Tate constructions, partition complexes and the Balmer spectrum of finite G-spectra.

This is joint work partly with Barthel, Nikolaus, Naumann, Noel, and Stapleton, and partly with Barthel and Greenlees.