Timeline for Fracture Squares of Bousfield Localizations of Spectra
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 25, 2014 at 15:17 | answer | added | Urs Schreiber | timeline score: 3 | |
| Oct 29, 2012 at 15:40 | answer | added | Nick Kuhn | timeline score: 7 | |
| Mar 13, 2012 at 14:33 | vote | accept | Jonathan Beardsley | ||
| Mar 13, 2012 at 6:39 | answer | added | Neil Strickland | timeline score: 13 | |
| Mar 12, 2012 at 22:44 | comment | added | Jonathan Beardsley | So Tyler, doesn't that orthogonality mean that we glue together an E(n) local spectrum really easily from it's K(n) local pieces? | |
| Mar 12, 2012 at 22:40 | comment | added | Tyler Lawson | On the other hand, you have that $K(n) \wedge K(m)$ is contractible for $n \neq m$, and the same identity holds for their Bousfield classes. The situation you're describing actually relies on something special - namely, that for $n > m$ anything $K(m)$-local is $K(n)$-acyclic. | |
| Mar 12, 2012 at 22:26 | comment | added | Jonathan Beardsley | And yes... you're right about the composition, to build the $E(n)$ localizations. I guess... hmm, what am I saying. I guess it should be something like that. In that case, it should be like wedging right? Since that's how we build our $E(n)$'s? | |
| Mar 12, 2012 at 22:04 | comment | added | Tom Goodwillie | You seem to have your arrows backwards. And it's possible that the well-known case you are thinking of involves a composition $L_E\circ L_F$ rather than $L_{E\wedge F}$ or $L_{E\vee F}$. | |
| Mar 12, 2012 at 22:04 | comment | added | Jonathan Beardsley | As well as situations with the Morava $K$ and $E$ theories. | |
| Mar 12, 2012 at 21:43 | history | edited | Jonathan Beardsley | CC BY-SA 3.0 |
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| Mar 12, 2012 at 21:20 | comment | added | Jonathan Beardsley | I might add that there is the well known case where we do this with completion at primes and rationalization. I think... | |
| Mar 12, 2012 at 21:16 | history | asked | Jonathan Beardsley | CC BY-SA 3.0 |