Timeline for Does a locally free sheaf over a product pushforward to a locally free sheaf?
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
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| Mar 17, 2010 at 22:13 | comment | added | BCnrd | @Torsten: It's fine with me if you delete my comment and your comments, if you wish to do so. | |
| Mar 17, 2010 at 5:25 | comment | added | Torsten Ekedahl | Mea culpa. My comment was wrong in almost any respect. I leave it both in order to leave the subsequent comment meaningful and as a reminder to myself. | |
| Mar 17, 2010 at 0:04 | comment | added | BCnrd | By Bass' theorem, a non-finitely generated projective module over any noetherian ring with connected spectrum is free. | |
| Mar 16, 2010 at 22:04 | comment | added | Torsten Ekedahl | I think the question may be based on the fact that for non-finitely generated modules projective and locally finite are not the same thing. Take for instance an elliptic curve (minus the origin to make it affine) and take the sum of all the line bundles (one for each point on the original elliptic curve). Then this sum is projective but there is no non-empty open subset of the spectrum over which it is free. | |
| Mar 16, 2010 at 21:28 | comment | added | Jan Weidner | Thanks, I edited my post. O_Y=\oplus k is true since O_Y is a k algebra and any vectorspace is free. | |
| Mar 16, 2010 at 21:27 | history | edited | Jan Weidner | CC BY-SA 2.5 |
added 70 characters in body
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| Mar 16, 2010 at 21:15 | comment | added | Georges Elencwajg | In the affine setting a locally free sheaf corresponds (under mild finiteness conditions) to a projective module, not to a free module. Also, your equality O_Y=\oplus k is incorrect. | |
| Mar 16, 2010 at 20:48 | history | answered | Jan Weidner | CC BY-SA 2.5 |