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Timeline for Statements reliant on conjectures

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Dec 25, 2015 at 1:12 comment added Joe Silverman Or even the Bombieri-Lang conjecture which says that if $K$ is a number field and $X/K$ is a variety of general type, then $X(K)$ is not Zariski dense in $K$. This is the special case of Vojta's conjecture (formulated earlier) applied to a variety of general type. Among it's numerous consequences is that among all curves $C/K$ of a fixed genus, there is an upper bound for $\#C(K)$ that is independent of $C$. (Due to Caparaso-Mazur-Harris.)
Jun 20, 2010 at 7:18 history answered Arturo Magidin CC BY-SA 2.5