Timeline for Flatness of modules over dual numbers
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 6, 2019 at 20:59 | comment | added | Chen | @JasonStarr and Phil: Thank you for the comments. I was considering $M'$ as an $\mathcal{O}_X$-module. | |
| Feb 5, 2019 at 14:50 | comment | added | Jason Starr | @PhilTosteson. I agree with you. As formulated, the OP seems to be asking whether $M'$, considered as an $\mathcal{O}_X$-module, is then flat when considered as an $\mathcal{O}_{X_D}$-module, and the answer to that question is "no". However, if the OP changes the $\mathcal{O}_{X_D}$-module structure as in my comment, then $M'$ is flat as an $\mathcal{O}_{X_D}$-module. | |
| Feb 5, 2019 at 14:41 | comment | added | Phil Tosteson | As worded I think Chen is not asking for that, and so the answer is no. | |
| Feb 5, 2019 at 13:20 | comment | added | Jason Starr | Your formulation is unclear. Is the action of $t$ on $M'$ intended to be the composition of the epimorphism $M'\to M$ and the monomorphism $M\to M'$? | |
| Feb 5, 2019 at 11:39 | history | asked | Chen | CC BY-SA 4.0 |