Timeline for Formal Group Laws on Ring Spectra?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 31, 2011 at 20:33 | answer | added | Sean Tilson | timeline score: 5 | |
| Dec 31, 2011 at 19:37 | comment | added | Jonathan Beardsley | Yeah actually I think what I'm asking is significantly different from the correspondence you mention, though it may not be of any relevance anyway. | |
| Dec 31, 2011 at 19:21 | comment | added | Jonathan Beardsley | Yeah I guess you're right. The analogy already exists as MU. But I wonder about HL nonetheless. | |
| Dec 31, 2011 at 19:19 | comment | added | David White | I agree with Dylan here, from what I've heard, the analog of a formal group law on ring spectra is $f:MU\rightarrow E$, i.e. a complex orientation. I think the Landweber Exact Functor Theorem is used to prove this is the ``right'' analog. Have you looked at Jacob Lurie's notes on Chromatic Homotopy Theory? math.harvard.edu/~lurie/252x.html | |
| Dec 31, 2011 at 16:37 | comment | added | Dylan Wilson | Classically, the analog would be where you replace $L$ by $MU$ and ask for a map $MU \rightarrow E$. This is equivalent to having a complex oriented ring spectrum. I'm not exactly sure what the "Landweber Exact Functor Theorem" would say here: as far as I know the Landweber exact functor theorem is already a statement involving spectra, so to have an "analog" you would need to fill in the analogy "(rings):(ring spectra):: (ring spectra): (???)"... and I don't know how to do that. | |
| Dec 31, 2011 at 15:24 | history | asked | Jonathan Beardsley | CC BY-SA 3.0 |