<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Brian Lehmann</style></author><author><style face="normal" font="default" size="100%">David McKinnon</style></author><author><style face="normal" font="default" size="100%">Matthew Satriano</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Approximating rational points on surfaces</style></title><secondary-title><style face="normal" font="default" size="100%">Proceedings of the American Mathematical Society</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2025</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://arxiv.org/abs/2403.02480</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">153</style></volume><pages><style face="normal" font="default" size="100%">1903-1915</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;MsoPlainText&quot;&gt;
	Let X&amp;nbsp;be a smooth projective algebraic variety over a number field k&amp;nbsp;and P&amp;nbsp;in X(k). In 2007, the second author conjectured that, in a precise sense, if rational points on X&amp;nbsp;are dense enough, then the best rational approximations to P&amp;nbsp;must lie on a curve. We present a strategy for deducing a slightly weaker conjecture from Vojta's conjecture, and execute this strategy for the full conjecture for split surfaces.
&lt;/p&gt;
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