Timeline for The cooperations algebras Johnson-Wilson theory and truncated BP-theory
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Nov 16, 2015 at 12:20 | comment | added | CWcx | @denis what you're describing is more or less how I computed $E(1)_*E(1)$, but I guess I am more curious in various relations that hold in $E(n)_*E(n)$. Based on some fiddling around I did, it seems hard to come up with explicit relations since the right unit is famously difficult to calculate. | |
| Nov 16, 2015 at 12:13 | comment | added | CWcx | @sean yes you're absolutely right! Thanks for pointing out my mistake :). I guess the right thing to say is that its the cofibre of the regular sequence $v_{n+1}, v_{n+2}, ...$. | |
| Nov 16, 2015 at 11:48 | comment | added | Sean Tilson | Your description of $BP\langle n \rangle$ as the connective cover of $E(n)$ is incorrect as they do not have the same $\pi_0$. For example, $\frac{v_1^{p^n-1}}{v_n}$ is in the homotopy of the connective cover of $E(n)$ but not in the homotopy of $BP\langle n \rangle$. I do not think this effects what anyone has said though. | |
| Nov 15, 2015 at 15:06 | answer | added | Drew Heard | timeline score: 5 | |
| Nov 14, 2015 at 17:49 | comment | added | Denis Nardin | In fact I think we can say more: $E(n)_*BP(m) = E(n)_*\otimes_{BP_*}BP_*BP(m) = E(n)_*\otimes_{BP_*}BP(m)_*BP$, so the only thing left to figure out is the map $BP_*\to BP(m)_*BP$, which should be related to the comultiplication on $BP_*$. | |
| Nov 14, 2015 at 17:40 | comment | added | Denis Nardin | Well the $E(n)$s are Landweber exact so $E(n)_*E(m)$ is just the scheme representing isomorphisms of their respective formal group laws. | |
| Nov 14, 2015 at 17:37 | review | First posts | |||
| Nov 14, 2015 at 17:55 | |||||
| Nov 14, 2015 at 17:36 | history | asked | CWcx | CC BY-SA 3.0 |