Timeline for Deformations of the punctured affine plane
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Mar 12, 2021 at 23:35 | vote | accept | Peter Scholze | ||
| Jan 22, 2013 at 11:04 | answer | added | Peter Scholze | timeline score: 13 | |
| Jan 14, 2013 at 20:59 | comment | added | Peter Scholze | @Angelo: Thanks for answering the second question, anyway! | |
| Jan 14, 2013 at 20:51 | comment | added | Angelo | To Jason: I am never 100% sure I am correct, because I have a tendency to overlook key points; so, the question was not completely rhetorical. To Peter: no reason to be sorry. | |
| Jan 14, 2013 at 20:34 | history | edited | Peter Scholze | CC BY-SA 3.0 |
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| Jan 14, 2013 at 20:33 | comment | added | Peter Scholze | Whoops. Sorry :-). | |
| Jan 14, 2013 at 20:22 | comment | added | Jason Starr | @Angelo: I realize that your question is rhetorical. Perhaps not everybody realizes this. Of course you are correct (as surely you already know). One relevant reference is Proposition 5.10.14, p. 119 of EGA IV_2 (presumably also "Local cohomology", Grothendieck-Hartshorne, etc.). | |
| Jan 14, 2013 at 20:15 | comment | added | Angelo |
If $R$ is a complete intersection it is Cohen-Macaulay; it follows that $R$ is the set of sections of the structure sheaf of $\mathop{\rm Spec}R \smallsetminus \{x\}$, since $\{x\}$ has codimension 2. Am I missing something?
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| Jan 14, 2013 at 20:03 | comment | added | Peter Scholze | No -- it is not true in general that $R$ is the set of global sections of $\mathrm{Spec} R$ - $x$. One example (which is of course not a complete intersection) is $R=k[X^2,X^3,XY,Y^2,Y^3]\subset k[X,Y]$. You might also have nilpotents at $x$. | |
| Jan 14, 2013 at 17:37 | comment | added | Angelo | About question 2, doesn't it follow by taking global sections of the structure sheaf that $R = k[x,y]$? | |
| Jan 14, 2013 at 16:35 | history | asked | Peter Scholze | CC BY-SA 3.0 |