Timeline for Fields in Stable Homotopy Theory
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Nov 6, 2013 at 14:38 | comment | added | Jonathan Beardsley | @DylanWilson why restrict oneself to flat extensions? I'm saying for arbitrary $R$, look at the $R$-local category, and ask for spectra which satisfy any of those criteria. There are obviously a few cases where this is known (localize at $K(n)$, or $E_n$, or $BP$). | |
| Nov 6, 2013 at 14:34 | comment | added | Jonathan Beardsley | @EricWofsey but every module over $K(n)$ is a wedge of $K(n)$'s yes? | |
| Nov 6, 2013 at 4:51 | comment | added | Dylan Wilson | I think the answer to this question is essentially "no". There's some recent work of Gepner-Antieau where you can take a flat extension of the sphere spectrum (there aren't many of these- mostly they look like "take a flat extension of the integers and tensor up to S") and then the fields you get are, no surprise, the Morava K-theories and the residue fields of pi_0 of your flat extension. | |
| Nov 6, 2013 at 4:02 | comment | added | Eric Wofsey | Your first sentence isn't quite true: what is the case is that any field is a module over some $K(n)$ (including $K(0)=H\mathbb{Q}$ and $K(\infty)=H\mathbb{F}_p$). For instance, for $p>2$, the mod $p$ $K$-theory spectrum is not equal to $K(1)$ but is a module over $K(1)$. | |
| Nov 6, 2013 at 3:56 | comment | added | Jonathan Beardsley | I suspect the answer is uninteresting for harmonic spectra. | |
| Nov 6, 2013 at 1:41 | history | edited | Ricardo Andrade |
added top level tag
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| Nov 6, 2013 at 0:40 | history | asked | Jonathan Beardsley | CC BY-SA 3.0 |