Timeline for Dualizing sheaf in mixed characteristic for regular schemes.
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Mar 10, 2013 at 21:57 | comment | added | rghthndsd | I forgot to include: if you have a reference without using dualizing complex, this would be preferred, but not required. | |
| Mar 10, 2013 at 17:32 | comment | added | rghthndsd | The specific properties like local/global duality would be more helpful to me. The $X$ I have in mind is quasi-projective. | |
| Mar 6, 2013 at 14:15 | comment | added | user30180 | Typo: "permitted to use dualizing" | |
| Mar 6, 2013 at 14:14 | comment | added | user30180 | Do you want a reference just that such Ext's glue to make a sheaf, or that it also has specific useful properties (such as for global duality or local duality)? And is the reference permitted to dualizing complexes? Is your $X$ of interest projective or quasi-projective? | |
| Mar 5, 2013 at 14:40 | comment | added | rghthndsd | Thanks, this is exactly what I was looking for. Do you have a reference for this? | |
| Mar 5, 2013 at 2:31 | comment | added | user30180 | Typo: $\Omega^{d_i}_{Y_i/R}$ should be $\Omega^{n_i}_{Y_i/R}$ above. | |
| Mar 5, 2013 at 2:30 | comment | added | user30180 | Assume $X$ is faithfully flat over the base dvr $R$ (or else you're over a field), and connected so the fibers of $X$ over Spec($R$) have a common pure dimension $d$. Any affine open in $X$ is Zariski-closed in an affine space over $R$, so more generally consider an open cover of $X$ by opens $U_i$ which admit closed immersions $j_i:U_i \hookrightarrow Y_i$ over $R$ where $Y_i$ is $R$-smooth of pure relative dimension $n_i$. Then ${\mathcal{Ext}}^{n_i-d}_{Y_i}(O_{U_i},\Omega^{d_i}_{Y_i/R})$ is a coherent $O_{U_i}$-module and these glue (very indirectly!) to give $\omega_{X/R}$. | |
| Mar 5, 2013 at 1:22 | history | edited | rghthndsd | CC BY-SA 3.0 |
edited title
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| Mar 5, 2013 at 0:02 | history | asked | rghthndsd | CC BY-SA 3.0 |