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 characterization of all thick subcategories of the stable homotopy category of p-local finite spectra.
This is a consequence of the nilpotence theorem.
For , write for the Morava K-theory spectrum.
Say that a -local finite spectrum has type if but for all . (e.g. Lurie, def. 6).
Write 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 are precisely the full subcategories on the spectra of type , for some . (e.g. Lurie, theorem 8).
In other words, the thick subcategories are the kernels of (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 August 22, 2024 at 12:00:32. See the history of this page for a list of all contributions to it.