Timeline for A homotopyish Landweber exact functor theorem
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Jun 5, 2012 at 2:00 | comment | added | Akhil Mathew | Whoops, I omitted a subscript and meant $\pi_* X \otimes_{MU_*} M_*$ (where $M_*$ is a graded module over $MU_*$). I will think some more about the lemma you mentioned, thogh. Thanks. | |
| Jun 3, 2012 at 20:16 | comment | added | Peter May | Steve, sorry about the etiquette of answers vs comments; can't expect an old guy to notice such distinctions. Akhil, I didn't say this is obvious. The paper is on my web page, [102], and the proof takes under two pages (because the serious math is in the references), but it probably shouldn't be repeated here. I can't answer your question precisely because I don't know what you mean by $MU_*M_*$, but here is the key lemma: If $X$ is an $R$-module, where $R$ is a commutative $S$-algebra such that $R_*R$ is $R_*$-flat, then the Hurewicz map gives $X_*$ a structure of $R_*R$-comodule. | |
| May 28, 2012 at 3:58 | comment | added | Akhil Mathew | I'm a little confused here. Shouldn't the condition for all finite $MU$ modules be related to flatness over $\pi_* MU$, because one is asking about $\pi_* X \otimes MU_* M_*$ rather than $MU_*(X) \otimes MU_* M_*$ (i.e., in the usual LEFT a comodule structure is being used which doesn't seem to exist here)? Also, I'm not seeing how this is obvious; could you perhaps clarify? | |
| May 26, 2012 at 23:00 | comment | added | Steve D | Perhaps this should be a comment on your original answer, rather than a separate answer? | |
| May 26, 2012 at 21:37 | history | answered | Peter May | CC BY-SA 3.0 |