symmetric monoidal (∞,1)-category of spectra
For each prime $p \in \mathbb{N}$ and for each natural number $n \in \mathbb{N}$ there is a Bousfield localization of spectra
where $E(n)$ is the $n$th Morava E-theory (for the given prime $p$). These arrange into the chromatic tower which for each spectrum $X$ is of the form
The homotopy fibers of each stage of the tower
is called the $n$th monochromatic layer of $X$.
Discussion of the first chromatic layer of the sphere spectrum is due to (Miller-Ravenel-Wilson 77). Review is in (Knudsen 13). This is the image of the J-homomorphism.
General lecture notes include
Discussion of the chromatic layers of the sphere spectrum is in
Lecture notes on this include
Johan Konter, The $K(n)$-local sphere, talk at Talbot 2013: Chromatic homotopy theory (pdfS.pdf))
Drew Heard, Resolutions of the $K(2)$-local sphere, talk at Talbot 2013: Chromatic homotopy theory (pdf)
Last revised on November 18, 2013 at 06:30:21. See the history of this page for a list of all contributions to it.