Timeline for Does smooth and proper over $\mathbb Z$ imply rational?
Current License: CC BY-SA 3.0
12 events
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| Jul 22, 2023 at 19:46 | comment | added | LSpice | @inkspot, re, you can! | |
| Jul 22, 2023 at 19:45 | comment | added | LSpice | @KevinBuzzard's hint referenced in the answer. | |
| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Jan 9, 2016 at 16:07 | comment | added | Daniel Litt | To get a scheme it suffices to find a vector bundle on $\overline{M_{g,n}}$ so that the stabilizer at every geometric point acts faithfully on its projectivization. I would expect a high-order jet bundle to work... | |
| May 17, 2012 at 15:40 | vote | accept | Ben Wieland | ||
| May 16, 2012 at 14:32 | comment | added | Ben Wieland | Does the non-tame inertia mean that they could have more general cohomology? But in practice, known cohomology classes, like Delta, don't violate restrictions on cohomology that could appear in schemes? | |
| May 16, 2012 at 13:04 | history | edited | Dan Petersen | CC BY-SA 3.0 |
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| May 16, 2012 at 11:25 | comment | added | inkspot | Ah, you intended (as I should have realized, sorry) "is finitely covered by" rather than "is a finite cover of". | |
| May 16, 2012 at 11:12 | comment | added | Dan Petersen | @inkspot you're right, this seems much more delicate than I thought. Indeed every explicit construction of such a cover that I know of uses some kind of non-abelian level structure, which doesn't work over the integers. I have to run to a seminar but I'll edit the answer later. | |
| May 16, 2012 at 10:16 | comment | added | inkspot | @Dan, please can you expand your remark that ${\overline M}_{g,n}$ is a finite cover of a smooth proper scheme (besides projective space)? As you say, it is a smooth Deligne-Mumford stack, but the inertia is not always tame, which, maybe, makes it not morally equivalent to a smooth proper scheme. | |
| May 16, 2012 at 8:17 | history | edited | Dan Petersen | CC BY-SA 3.0 |
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| May 16, 2012 at 8:10 | history | answered | Dan Petersen | CC BY-SA 3.0 |