group cohomology, nonabelian group cohomology, Lie group cohomology
cohomology with constant coefficients / with a local system of coefficients
differential cohomology
symmetric monoidal (∞,1)-category of spectra
What is called the thick subcategory theorem gives a a characterization of all thick subcategories of the stable homotopy category of p-local finite spectra.
This is a consequence of the nilpotence theorem.
For $n \in \mathbb{N}$, write $K(n)$ for the Morava K-theory spectrum.
Say that a $p$-local finite spectrum $X$ has type $n$ if $K(n)_\ast(X) \neq 0$ but $K(k)_\ast(X) \simeq 0$ for all $k \lt n$. (e.g. Lurie, def. 6).
Write $Spectra^{fin}_p \hookrightarrow Spectra$ be the full subcategory of the (infinity,1)-category of spectra on the p-local finite spectra.
The thick subcategory theorem says that thick subcategories of $Spectra^{fin}_p$ are precisely the full subcategories on the spectra of type $\lt n$, for some $n$. (e.g. Lurie, theorem 8).
In other words, the thick subcategories are the kernels of $K(n)_\ast$ (for any given prime).
The thick subcategory theorem serves to determine the prime spectrum of a symmetric monoidal stable (∞,1)-category of the stable homotopy theory.
(For an exposition see MazelGee 13, around slide 9).
The original article is
Further discussion is in
Alain Jeanneret, Peter Landweber, Douglas Ravenel, A note on the thick subcategory theorem (pdf)
Jacob Lurie, Chromatic Homotopy Theory, lecture 26, Thick subcategories (pdf)
Some big-picture motivation is in
Last revised on March 25, 2014 at 01:31:26. See the history of this page for a list of all contributions to it.