Timeline for On Zariski Dense Subsets
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Jun 4, 2011 at 9:18 | comment | added | JSpecter | In order to generalize this example to the case of an arbitrary algebraically closed field $k$ of characteristic 0, all that must be done is to redefine $U$ to be the set of pairs $(x,2^x)$ where $x\in\mathbb{Z}$. Then an identical argument as used above shows that any infinite subset $U′$ of $U$ is not contained in the vanishing of any nonzero polynomial in $\overline{\mathbb{Q}}[X,Y]$. As $U$ is contained in $\mathbb{A}^2(\mathbb{Q})$, it follows $U′$ is not contained in the vanishing of any nonzero polynomial in $k[X,Y]$. The claim then follows via Tom Goodwillie's succinct argument. | |
| Jun 2, 2011 at 18:06 | comment | added | Tom Goodwillie | Second paragraph can be replaced by: Since every polynomial that vanishes on $U'$ vanishes at all points, all points are in $\bar {U'}$. | |
| Jun 2, 2011 at 15:03 | vote | accept | gummi | ||
| Jun 2, 2011 at 15:01 | history | edited | JSpecter | CC BY-SA 3.0 |
added 320 characters in body
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| Jun 2, 2011 at 14:26 | history | answered | JSpecter | CC BY-SA 3.0 |