Timeline for Comparing heights of rational points on curves through covers
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Oct 4, 2011 at 9:19 | vote | accept | Showmie | ||
| Oct 3, 2011 at 23:43 | answer | added | Joe Silverman | timeline score: 3 | |
| Oct 3, 2011 at 21:09 | comment | added | ACL | Since you assume $Y\simeq \mathbf P^1$, it is more natural to give yourself $\pi$ as a rational function of some degree $d$. Then, there are effective constants $c$ and $c'$ such that $ d h(y) -c \leq h(\pi(y)) \leq d h(y)+c'$ for all $y\in \mathbf P^1(\overline{\mathbf Q})$. The constant $c'$ is easy to obtain. The effectivity of $c$ is more subtle (one can get one through resultants, but in a more general setting, some form of effective Nullstellensatz is necessary). | |
| Oct 3, 2011 at 13:05 | history | edited | Showmie | CC BY-SA 3.0 |
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| Oct 3, 2011 at 11:03 | history | edited | Showmie | CC BY-SA 3.0 |
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| Oct 3, 2011 at 9:10 | comment | added | Damian Rössler | What do you mean by the "naive height of b" ? (a Weil height depends on a line bundle). ALso, I think $\pi=f$ in your post. | |
| Oct 3, 2011 at 8:54 | history | asked | Showmie | CC BY-SA 3.0 |