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
A statement in chromatic homotopy theory about periodicity of p-local spectra.
A $v_n$-self-map on a p-local finite spectrum $X$, for $n \geq 1$ is a map
such that
it induces an isomorphism $K(n)_\ast X \longrightarrow K(n)_\ast X$
for $n \neq l$ the induced map $K(l)_\ast X \longrightarrow K(l)_\ast X$ is nilpotent.
The periodicity theorem says:
Any p-local finite spectrum $X$ admits a $v_n$-self-map. (Lurie 10, theorem 4)
It is a corollary of the theorem, that for any such space, there is a $v_n$-self-map, such that for $n \neq l$ the induced map $K(l)_\ast X \longrightarrow K(l)_\ast X$ is $0$, and not just nilpotent. (Hopkins, Smith, Corollary 3.3)
The periodicity theorem is due to
A quick review is in
Lecture notes are in
Quick lecture notes are in
Last revised on March 24, 2018 at 12:28:33. See the history of this page for a list of all contributions to it.