Timeline for Formally étale at all primes does not imply formally étale?
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 11, 2010 at 19:51 | history | made wiki | Post Made Community Wiki by Anton Geraschenko | ||
| Feb 23, 2010 at 12:20 | comment | added | JBorger | Whoops, my mistake. I misread the question. Thanks for the correction. | |
| Feb 23, 2010 at 11:46 | comment | added | Harry Gindi | In particular, if $S=R_Q$ and for every prime $\mathfrak{p}$ of $S$, $S_{\mathfrak{p}}$ is formally étale over $R$, but $S$ only has one maximal ideal, and localizing at this maximal ideal gives us an isomorphic ring since we're localizing away units, so in particular $S_Q$=$R_Q$, which is then by assumption formally étale. | |
| Feb 23, 2010 at 11:42 | comment | added | Harry Gindi | We're not looking for étale, we're looking for formally étale. So it just has to satisfy the nilpotent lifting properties. | |
| Feb 23, 2010 at 11:27 | history | answered | JBorger | CC BY-SA 2.5 |