# Applications of equivariant homotopy theory in chromatic homotopy theory

I usually do computations in equivariant homotopy theory, but I would like to learn chromatic homotopy theory where one may use the equivariant techniques, e.g., slice spectral sequences, etc.

For this, I am looking for those papers which are dealt with the above kind of literature.

Any reference will be highly appreciated.

• Several results used equivariant methods in the context of algebraic K theory, and in particular for work related to the redshift conjecture (this is where chromatic homotopy enters). Not sure if they use the kind of tools you are looking for. For example arxiv.org/abs/2011.08233 and arxiv.org/abs/1606.03328 Dec 25, 2020 at 16:09
• @ShayBenMoshe: Thank you for the comment. I will go through these articles. Dec 26, 2020 at 2:34

Beside that amazing paper, equivariant homotopy theory can be used in the computation of Picard groups of some local categories. For example the following paper uses $$C_4$$-equivariant homotopy theory to study the Picard group of the $$K(2)$$-local category
Beaudry, Agnes, Irina Bobkova, Michael Hill, and Vesna Stojanoska. "Invertible $$K (2)$$-Local $$E$$-Modules in $$C_4$$-Spectra." (arXiv:1901.02109) (2019).
In both cases the intuition is that equivariant techniques are useful to run descent arguments along a Galois extension (typically by some small subgroup of the Morava stabilizer group). For example the slice spectral sequence allows one to resolve Borel $$G$$-spectra (i.e. "spectra with a $$G$$-action") by pieces that are not Borel anymore but which are "simpler" in some sense.