Search Results

Charles and Tom have answered question (2) very nicely. For question (1), for discussing inequalities like $\langle F \rangle \leq \langle E \rangle$, it doesn't matter too much which point of view y …

The spectrum $H\mathbf{F}_p$ is an acyclic for both $\bigvee \langle T(n) \rangle$ and $\bigvee \langle K(n) \rangle$. Therefore neither of these wedges equals $\langle S \rangle$.

Bousfield, in his paper "The Boolean algebra of spectra" (Comm Math Helv 54, 368–377 (1979), https://doi.org/10.1007/BF02566281), defined $\mathbf{DL}$, a sublattice of the Bousfield lattice, to consi …

Neil's answer is great. I just wanted to add that in fact the Bousfield classes of the Morava $K$-theories are minimal non-zero classes in the Bousfield lattice. In particular, $\langle K(n) \rangle$ …

Finite localizations, as defined by Miller ("Finite localizations", Boletin de la Sociedad Matematica Mexicana 37 (1992), 383–390; preprint here) are also smashing localizations. The finite localizati …

If you're looking for a reference in print, it's in Ravenel's book Complex Cobordism and Stable Homotopy Groups of Spheres. See the comments after the proof of Theorem A2.2.18. (This book is availab …

As Dave Benson says, the Noetherian condition simplifies a lot of things. The derived category of a commutative ring satisfies many of the properties of the stable homotopy category. The derived categ …

I have a guess for question 1. Fix $n \geq 0$ and let $E(n)$ be the Hopf subalgebra dual to $\mathbb{F}_2 [\xi_{n+1}, \xi_{n+2}, \dots] / (\xi_i^{2^{n+1}})$. Every $x\in E(n)$ satisfies $x^2=0$, and m …

The red dot in (3,0) comes from a map $\Sigma^3 D \to \mathbb{F}_2$, and this map is the image of a map $\mathbb{R}P^\infty \to \mathbb{F}_2$, so it goes to zero under the coboundary map. This agrees …

This is not a complete answer, but it is too long for a comment. I will assume you are interested in the spectral sequences in Section 8 of Adams, not the Atiyah-Hirzebruch spectral sequences of Secti …