Timeline for Principal G-covers with G finite abelian
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Jul 9, 2012 at 11:13 | vote | accept | calc | ||
| Jul 6, 2012 at 7:34 | comment | added | calc | Most important thing: Thank you and Will very much for your answers! | |
| Jul 6, 2012 at 7:22 | comment | added | calc | As for the spectral sequence. It would be enough (using the exact sequence in low degrees) to prove that 1) $Ext^1(G^{\vee},\mathcal{O}_X^*)$ equals $Hom(G^{\vee},H^1(\mathcal{O}_X^*)$ 2)Vanishing of $H^0(\mathcal{E}xt^1(G^{\vee}, \mathcal{O}_X^*))$. Are these true? | |
| Jul 5, 2012 at 20:41 | comment | added | Will Sawin | By the way, I also think a spectral sequence proof does exist. | |
| Jul 5, 2012 at 17:11 | comment | added | Jason Starr | Remark 1.3.1, p. 84, of "Enriques Surfaces" by Cossec and Dolgachev gives this result also. They fram this as part of "Cartier duality". | |
| Jul 5, 2012 at 17:02 | history | edited | Sam Gunningham | CC BY-SA 3.0 |
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| Jul 5, 2012 at 15:46 | comment | added | Will Sawin | I don't understand how your first claim is related to the Kummer exact sequence at all. The isomorphism is an isomorphism of presheaves as well as sheaves because it is defined on every open set, since field extensions of $\mathbb C$ don't give you any new characters of a group. | |
| Jul 5, 2012 at 13:29 | history | edited | Sam Gunningham | CC BY-SA 3.0 |
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| Jul 5, 2012 at 13:15 | history | answered | Sam Gunningham | CC BY-SA 3.0 |