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<a accesskey="3" href="page.php?w=Uniform_boundedness_conjecture_for_rational_points&amp;p=2">3.Next</a>
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<p>In <a href="page.php?w=arithmetic_geometry">arithmetic geometry</a>, the <b>uniform boundedness conjecture for rational points</b> asserts that for a given <a href="page.php?w=number_field">number field</a>  and a positive integer , there exists a number  depending only on  and  such that for any <a href="page.php?w=algebraic_curve">algebraic curve</a>  defined over  having <a href="page.php?w=Geometric_genus">genus</a> equal to  has at most  -<a href="page.php?w=rational_point">rational point</a>s. This is a refinement of <a href="page.php?w=Faltings%27_theorem">Faltings' theorem</a>,</p><p>
<a accesskey="3" href="page.php?w=Uniform_boundedness_conjecture_for_rational_points&amp;p=2">3.Next</a>
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