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3
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204 views

Fields in Stable Homotopy Theory

It is known that the only "fields" in stable homotopy theory, after localizing at a prime $p$, are Eilenberg-Mac Lane spectra for fields and the Morava K-theories (this is true in a few senses: these ...
2
votes
0answers
110 views

Formal n-buds from BU(n) rather than SU(n)

It's known, from Ravenel's green book, as well as other sources, that we build formal group laws over a ring from n-buds, where an n-bud is essentially a truncated formal group law (sometimes called a ...
10
votes
1answer
509 views

Connection of X(n) spectra to formal group laws

In the proof of the Nilpotence Theorem, or at least in Ravenel's account of it in his Orange Book, a sequence of spectra are used, denoted $X(n)$ with $X(0)=\mathbb{S}$ and and $X(\infty)=MU$ such ...
2
votes
1answer
176 views

Compact MU or BP Modules

Is there a classification of the compact MU or BP modules in any category of spectra? Can the periodicity theorem be finagled to give a MU-module structure on finite spectra?
4
votes
1answer
168 views

Localization at Infinite Wedges of K-theories or BP

This is basically a reference request. Does anyone know if the structure of the homotopy category of spectra (or maybe just the model, i.e. w/o the homotopy, category), localized at infinite wedges ...
1
vote
1answer
143 views

Properties of endmorphism rings of E(n),K(n)-localized spheres

Is it known whether or not the endomorphism rings (or ring spectra) of the localized sphere spectra in $L_nSp$ and $L_{K(n)}Sp$ are Noetherian or not? Are they well understood? Perhaps, in the vein of ...