Timeline for Reflexive sheaf and flatness
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 9, 2016 at 19:25 | comment | added | Ron | @Mohan Sorry. I have removed my previous comments. The original question that I had was: I took a coherent pure sheaf $\mathcal{F}$ on $X$ flat over $Y$ of rank $n$. I wanted to ask if $(\wedge^n \mathcal{F})^{\vee \vee}$ is flat over $Y$. In my cases, $X$ is of the form $Y \times X'$ where $X'$ is integral, normal of dimension at least $1$. | |
| Mar 9, 2016 at 19:20 | comment | added | Mohan | If $X=Y$ as in my example, $F$ is coherent on $Y$ since it is so on $X$. | |
| Mar 9, 2016 at 19:19 | comment | added | Mohan | For any reasonable Noetherian scheme , double dual of a coherent sheaf is coherent. | |
| Mar 9, 2016 at 19:13 | comment | added | Mohan | First, an example. Take $X=Y$ smooth, $f=Id$. Then, flatness means, the double dual should be locally free. Examples abound where this is false. For your second part, unless you suggest what kind of conditions on $f$ are you looking for, difficult to answer. | |
| Mar 9, 2016 at 18:46 | history | asked | Ron | CC BY-SA 3.0 |