Chromatic cohomology of finite groups

This page contains material for my lectures at the VIASM Winter School on Algebraic Topology and its Applications at Quy Nhơn University in Vietnam.

Talks

Talk 1 (screen, print): Generalised cohomology, formal groups.
Talk 2 (screen, print): The Lazard ring, Quillen's Theorem, Morava $K$-theory and $E$-theory of abelian groups, characteristic classes.
Talk 3 (screen, print): Flag manifolds, finiteness results, groupoids, generalised characters, divisors and vector bundles, level structures.
Talk 4 (screen, print): Duality, transfer, Tate vanishing, the abelian case, $\lambda$-semirings, Chern approximations, the example of $\Sigma_4$.
Talk 5 (screen, print): Symmetric groups and finite general linear groups.

Background

Notes on formal group theory
Notes on formal schemes

Literature

All extensions of $C_2$ by $C_{2^n}\times C_{2^n}$ are good for the Morava $K$-theory (Bakuradze 2020)
Morava $K$-theory rings for the groups $G_{38},\dots,G_{41}$ of order 32 (Bakuradze and Jibladze 2014)
Centralizers in good groups are good (Barthel and Stapleton 2016)
Transfer ideals and torsion in the Morava $E$-theory of abelian groups (Barthel and Stapleton 2020)
Ambidexterity in Chromatic Homotopy Theory (Carmeli, Schlank and Yanovski 2018}
Hall algebras, hereditary algebras and quantum groups (Green 1995)
The characters of the finite general linear groups (Green 1955)
The Tate spectrum of $v_n$-periodic complex oriented theories (Greenlees and Sadofsky 1996)
Varieties and local cohomology for chromatic group cohomology rings (Greenlees and Strickland 1999)
Generalized group characters and complex oriented cohomology theories (Hopkins, Kuhn and Ravenel 2000)
Ambidexterity in $K(n)$-local stable homotopy theory (Hopkins and Lurie 1999)
Chromatic (co)homology of finite general linear groups (Hutchinson, Marsh and Strickland 2021).
Section 1.2 of this paper contains a review of relevant literature.
Odd-degree elements in the Morava $K(n)$ cohomology of finite groups (Kriz and Lee 2000)
On the discrete representations of the general linear groups over a finite field (Lusztig 1973)
Modular isogeny complexes (Rezk 2012)
On Morava $K$-theories of Chevalley groups (Tanabe 1995)
A transchromatic proof of Strickland's theorem (Schlank and Stapleton 2015)
Morava $K$-theory of groups of order 32 (Schuster 2011)
$K(n)$ Chern approximations of some finite groups (Schuster 2012)
Subgroups of $p$-divisible groups and centralizers in symmetric groups (Stapleton 2015)
Transchromatic generalized character maps (Stapleton 2013)
Transchromatic twisted character maps (Stapleton 2015)
Finite subgroups of formal groups (Strickland 1997)
$K(N)$-local duality for finite groups and groupoids (Strickland 2000)
Chern approximations for generalised group cohomology (Strickland 2001)
Morava $E$-theory of symmetric groups (Strickland 1998)
HKR characters, $p$-divisible groups and the generalized Chern character (Torii 2010)