<?xml version="1.0" encoding='utf-8'?>
<!DOCTYPE wml PUBLIC "-//WAPFORUM//DTD WML 1.1//EN" "http://www.wapforum.org/DTD/wml_1.1.xml">
<wml>
<card id="card1" title="Uniform boundedness conjecture for rational points - Page 2 - Wikipedia">
<p>
<a accesskey="1" href="page.php?w=Uniform_boundedness_conjecture_for_rational_points&amp;p=1">1.Previous</a><br />
<a accesskey="3" href="page.php?w=Uniform_boundedness_conjecture_for_rational_points&amp;p=3">3.Next</a>
</p>
<p>which asserts that the set of -rational points  is necessarily finite.</p>

<p><big>Progress</big></p>
<p>The first significant progress towards the conjecture was due to <a href="page.php?w=Lucia_Caporaso">Caporaso</a>, <a href="page.php?w=Joe_Harris_%28mathematician%29">Harris</a>, and <a href="page.php?w=Barry_Mazur">Mazur</a>. They proved that the conjecture holds if one assumes the <a href="page.php?w=Bombieri-Lang_conjecture">Bombieri-Lang conjecture</a>.</p>

<p><big>Mazur's conjecture B</big></p>
<p><b>Mazur's conjecture B</b> is a weaker variant of the</p><p>
<a accesskey="1" href="page.php?w=Uniform_boundedness_conjecture_for_rational_points&amp;p=1">1.Previous</a><br />
<a accesskey="3" href="page.php?w=Uniform_boundedness_conjecture_for_rational_points&amp;p=3">3.Next</a>
</p>

<do type="prev" label="Search">
        <go href="search.wml"/>
</do>

</card>
</wml>
