Timeline for Are maximal Cohen-Macaulay modules supported everywhere?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 1, 2012 at 17:46 | comment | added | Mahdi Majidi-Zolbanin | As Graham's example shows, it's not true in general, but sometimes it's true. For example if $A$ is a domain and $M$ is finitely generated, then it's true, because if $M$ is maximal CM, then $\mathrm{dim}\ M = \mathrm{depth}\ M = \mathrm{dim}\ A$. If $I$ is the annihilator of $M$, then it follows $\mathrm{dim}\ A/I=\mathrm{dim}\ A$. Then since $A$ is a domain, $I=(0)$, and since $M$ is finitely generated, $\mathrm{Supp}(M)=V(I)=\mathrm{Spec}\:A$. | |
| Jan 1, 2012 at 17:29 | vote | accept | ashpool | ||
| Jan 1, 2012 at 17:14 | vote | accept | ashpool | ||
| Jan 1, 2012 at 17:26 | |||||
| Jan 1, 2012 at 16:58 | answer | added | Graham Leuschke | timeline score: 3 | |
| Jan 1, 2012 at 15:43 | history | asked | ashpool | CC BY-SA 3.0 |