Timeline for are these functors exact?
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Jun 1, 2013 at 23:39 | comment | added | Ben Wieland | Exactness is a local question. | |
| Jun 1, 2013 at 19:08 | comment | added | Jack Huizenga | If the divisor is not ample then it is not such a hyperplane section. For example the complement of a line on a quadric surface is a $\mathbb{P}^1$ bundle over $\mathbb{A}^1$. | |
| Jun 1, 2013 at 18:44 | comment | added | user19475 | I would guess so, since according to [Milne, Étale cohomology], Theorem VI.7.1, the complement in a projective variety of a hypersurface section is affine. | |
| Jun 1, 2013 at 18:38 | history | edited | user19475 | CC BY-SA 3.0 |
added 68 characters in body
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| Jun 1, 2013 at 18:35 | comment | added | exactfun | So now the question is: is $j$ affine in the situation "complement of a SNCD"? | |
| Jun 1, 2013 at 18:31 | comment | added | user19475 | This holds for $j: U \hookrightarrow X$ an open immersion. An affine morphism is exact. | |
| Jun 1, 2013 at 18:26 | comment | added | exactfun | Thanks, Timo? Is that general or you have taken into account the shape of $U$? Is the morphism $j$ affine or something that allows to conclude exactness? | |
| Jun 1, 2013 at 18:15 | history | answered | user19475 | CC BY-SA 3.0 |