Timeline for Ascent for projective modules
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 10, 2021 at 22:22 | comment | added | Badam Baplan | @Z.M You are of course right, your example is faithfully flat. You are also right that I was looking for domains, but I didn't say that in my question, which is my own fault! Your comment was enough to convince me that I don't care very much about this question, which is good enough. | |
| May 7, 2021 at 12:37 | comment | added | Z. M | I think that my example is already faithfully flat (it is surjective on Spec)? Anyway, I think that maybe you are interested in an example when $C$ is a domain (that seems more challenging)? | |
| May 7, 2021 at 6:10 | comment | added | Laurent Moret-Bailly | Just take $C=C_0\times B$ where $C_0$ is any counterexample. | |
| May 7, 2021 at 0:50 | comment | added | Badam Baplan | @Z.M Can you think of a counterexample with $C$ faithfully flat over $A$? | |
| May 7, 2021 at 0:46 | comment | added | Badam Baplan | @Z. M Yes that does the job. "Normalizing" in this case basically knocks out the localization component, which is precisely the obstruction to being projective | |
| May 7, 2021 at 0:26 | comment | added | Z. M | What about $A=\mathbb Z$, $B=\mathbb Z[T]$ and $C=B\times\mathbb Z[1/p]$ where $B\to C$ is induced by $T\mapsto(T,1/p)$? | |
| May 6, 2021 at 22:03 | history | asked | Badam Baplan | CC BY-SA 4.0 |