Timeline for Are Kahler differentials the same on the affine closure on a quasi-affine scheme?
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
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| Mar 6, 2011 at 15:08 | comment | added | Greg Muller | Heres a potential difficulty. Even if you can find an $\overline{X}$ with non-reflexive Kahler differentials, and an open subscheme $X$ whose complement is codim $\geq2$, it still is guaranteed that $\overline{X}=Spec(\Gamma(\mathcal{O}_X))$. For example, if the appropriate singular point is the intersection of two components, the affine closure of $X$ won't be $\overline{X}$, no matter how small the complement is. | |
| Mar 5, 2011 at 15:39 | history | edited | Sándor Kovács | CC BY-SA 2.5 |
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| Mar 5, 2011 at 15:35 | comment | added | Sándor Kovács | Karl, I think for the direction reflexive $\Rightarrow$ $S_2$ you don't need $G_1$. You need that for the converse. See a sketch above why. (And let me know if there is something wrong with it). | |
| Mar 5, 2011 at 15:34 | history | edited | Sándor Kovács | CC BY-SA 2.5 |
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| Mar 5, 2011 at 13:01 | comment | added | Karl Schwede | Sandor, on an S2 scheme, is it true that every reflexive sheaf is S2? I thought you needed S2 + G1 (do you know a reference?) | |
| Mar 5, 2011 at 6:53 | history | edited | Sándor Kovács | CC BY-SA 2.5 |
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| Mar 5, 2011 at 6:48 | comment | added | Sándor Kovács | @Qing Liu: I suppose I secretly assumed it was noetherian. | |
| Mar 5, 2011 at 1:00 | comment | added | Qing Liu | To work correctly with the depth, do you have to assume $\overline{X}$ is noetherian ? | |
| Mar 4, 2011 at 23:32 | history | edited | Sándor Kovács | CC BY-SA 2.5 |
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| Mar 4, 2011 at 23:26 | history | edited | Sándor Kovács | CC BY-SA 2.5 |
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| Mar 4, 2011 at 23:24 | comment | added | Sándor Kovács | On the other hand, it is almost equivalent to being reflexive. | |
| Mar 4, 2011 at 23:23 | comment | added | Greg Muller | Yes, Sandor, you are correct in that I explicitly want $\overline{X}=Spec(\mathcal{O}_X)$. And its true that, if we know $\Omega_{\overline{X}}$ is reflexive, then we are done. | |
| Mar 4, 2011 at 23:20 | history | edited | Sándor Kovács | CC BY-SA 2.5 |
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| Mar 4, 2011 at 23:15 | history | answered | Sándor Kovács | CC BY-SA 2.5 |