Timeline for Finitely-affine morphisms; cohomological dimension of schemes
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Nov 14, 2012 at 0:35 | history | edited | Qing Liu |
yet another typo
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| Nov 13, 2012 at 23:53 | history | edited | Qing Liu | CC BY-SA 3.0 |
typo
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| Nov 13, 2012 at 23:53 | answer | added | Qing Liu | timeline score: 3 | |
| Nov 12, 2012 at 10:29 | comment | added | Qing Liu | Yes they actually are interested in a different number. It would be interesting to start with a baby case: $X$ is quasi-projective over $U$ of relative dimension $1$. Then I think $n\le 2$. Can $X$ be covered by $2$ affine open subsets ? | |
| Nov 11, 2012 at 21:30 | comment | added | Leonid Positselski | Thank you for this helpful reference, which explains that a bound on the Krull dimension of a scheme (in fact, of a variety over a field), implying of course a bound on its cohomological dimension, still implies no bound on the number of covering open affines. However, this counterexample (attributed to Starr) is not a quasi-projective variety. The case I seem to be most interested in is when $X$ is quasi-affine, on the other hand. | |
| Nov 11, 2012 at 16:54 | comment | added | Qing Liu | You might have a look at "The Affine Stratification Number and the Moduli Space of Curves" by Mike Roth and Ravi Vakil. I don't knwon whether it answers your question though. | |
| Nov 11, 2012 at 16:21 | history | asked | Leonid Positselski | CC BY-SA 3.0 |