Timeline for Is there a Riemann-Roch for smooth projective curves over an arbitrary field?
Current License: CC BY-SA 2.5
8 events
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| Feb 17, 2011 at 14:44 | comment | added | Hugo Chapdelaine | You are probably right, but unfortunately, unless I'm mistaken, I thought that $k$ was assumed to algebraically closed in Hartshorne's book. Is there some tricky point to address in characteristic $p$ when $k$ is not perfect? | |
| Feb 16, 2011 at 7:29 | comment | added | Pete L. Clark | @Hugo: yes. (I would have answered your question by saying: "Yes. It's called the Riemann-Roch Theorem." None of the standard proofs use the algebraic closure of the ground field at any point. But the answers you have been given are somewhat more generous than this...) | |
| Feb 15, 2011 at 21:13 | history | edited | Georges Elencwajg | CC BY-SA 2.5 |
Added: Complement
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| Feb 15, 2011 at 18:08 | comment | added | Hugo Chapdelaine | Thanks a lot Georges for Qing Liu's reference. So what is the dualizing sheaf in general for a smooth projective curve defined over an arbitrary field $k$? Is it still the canonical line bundle? | |
| Feb 15, 2011 at 1:31 | comment | added | Georges Elencwajg | Of course Felipe is absolutely right about the German school's priority . However I find fascinating the ease and elegance with which schemes integrate all those classical results into their harmonious, coherent and powerful language. | |
| Feb 15, 2011 at 0:20 | history | edited | Georges Elencwajg | CC BY-SA 2.5 |
suppressed redundant word "book" that I had used twice
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| Feb 14, 2011 at 23:54 | history | edited | Georges Elencwajg | CC BY-SA 2.5 |
added reference for statement over artin ring
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| Feb 14, 2011 at 23:04 | history | answered | Georges Elencwajg | CC BY-SA 2.5 |