Timeline for Existence of points on varieties which avoid a given number field.
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Jun 12, 2012 at 6:47 | comment | added | Harry | The following MO thread might be relevant: mathoverflow.net/questions/77644/… | |
| Jun 12, 2012 at 1:19 | comment | added | Will Sawin | One can find a map to $\mathbb P^n$ by choosing a divisor of sufficient degree and applying Riemann-Roch. But of course you really need a $K$-rational map, which requires a $K$-rational divisor of prime degree, which need not exist. So gonality isn't really the issue with this argument. | |
| Jun 12, 2012 at 0:40 | vote | accept | David Zureick-Brown | ||
| Jun 12, 2012 at 0:39 | comment | added | David Zureick-Brown | @Will: That would do it. What is the map to P^n? | |
| Jun 11, 2012 at 23:36 | comment | added | Will Sawin | Are you sure your proof only works for prime gonality, and not when there exists nonconstant map of prime degree to $\mathbb P^1$. All curves have a nonconstant map of prime degree to $\mathbb P^1$, because they have a nonconstant map of prime degree to $\mathbb P^n$ and you can project down to $\mathbb P^1$. | |
| Jun 11, 2012 at 23:35 | answer | added | Olivier Benoist | timeline score: 8 | |
| Jun 11, 2012 at 22:52 | answer | added | user631 | timeline score: 13 | |
| Jun 11, 2012 at 20:09 | history | edited | David Zureick-Brown | CC BY-SA 3.0 |
deleted 56 characters in body
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| Jun 11, 2012 at 19:57 | history | edited | David Zureick-Brown | CC BY-SA 3.0 |
typo, added a short remark
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| Jun 11, 2012 at 19:51 | history | asked | David Zureick-Brown | CC BY-SA 3.0 |