Timeline for A morphism from proper to affine is constant?
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
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| Aug 7, 2010 at 22:39 | comment | added | BCnrd | Dear Qing: yep. | |
| Aug 7, 2010 at 22:09 | comment | added | Qing Liu | If $S$ is Noetherian affine and normal, and $X$ is normal, as $O(X_U)=O(U)$, then Zariski's extension theorem imply that $O(X)=O(S)$. I think this is reason why BCnrd said "try non-normal counterexample". The problem I think is to find $X$ flat over $S$. | |
| Aug 7, 2010 at 21:15 | history | edited | Angelo | CC BY-SA 2.5 |
edited body
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| Aug 7, 2010 at 17:18 | history | edited | Angelo | CC BY-SA 2.5 |
added 134 characters in body
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| Aug 7, 2010 at 16:28 | comment | added | Angelo | Oops sorry, I had missed the comment. | |
| Aug 7, 2010 at 16:19 | comment | added | BCnrd | Dear Angelo: The OP made the comment below the question that he only actually has properness over a dense open in $S$. So unfortunately the usual cohomological tools seem to not apply. I hope the OP will follow my request to please revise the question to include the hypotheses desired (and to make clear if U is quasi-compact over S, schematically or just topologically dense, etc.). | |
| Aug 7, 2010 at 16:11 | history | answered | Angelo | CC BY-SA 2.5 |