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Reference.org
Torsion conjecture
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<p>In <a href="/facts/Algebraic_geometry/rh7RHVp3">algebraic geometry</a> and <a href="/facts/Number_theory/zhoa7zrc">number theory</a>, the torsion conjecture or uniform boundedness conjecture for torsion points for <a href="/facts/Abelian_varieties/dGSDVruG">abelian varieties</a> states that the <a href="/facts/Order_(group_theory)/Cl3tKGFg">order</a> of the <a href="/facts/Torsion_group/TEvLhDtm">torsion group</a> of an abelian variety over a <a href="/facts/Number_field/e0K0TXSh">number field</a> can be bounded in terms of the <a href="/facts/Dimension_of_an_algebraic_variety/sXqIHcYc">dimension of the variety</a> and the number field. A stronger version of the conjecture is that the torsion is bounded in terms of the dimension of the variety and the degree of the number field. The torsion conjecture has been completely resolved in the case of <a href="/facts/Elliptic_curves/60jvaHSA">elliptic curves</a>. </p>