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Tate conjecture
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<p>In <a href="/facts/Number_theory/zhoa7zrc">number theory</a> and <a href="/facts/Algebraic_geometry/rh7RHVp3">algebraic geometry</a>, the Tate conjecture is a 1963 <a href="/facts/Conjecture/oPWUb7SF">conjecture</a> of <a href="/facts/John_Tate_(mathematician)/nBntLCG0">John Tate</a> that would describe the <a href="/facts/Algebraic_cycle/eY1eYyk3">algebraic cycles</a> on a <a href="/facts/Algebraic_variety/Vk7f97vn">variety</a> in terms of a more computable invariant, the <a href="/facts/Galois_module/fYDgqs8d">Galois representation</a> on <a href="/facts/%25C3%2589tale_cohomology/KXJ8a6Hw">étale cohomology</a>. The conjecture is a central problem in the theory of algebraic cycles. It can be considered an arithmetic analog of the <a href="/facts/Hodge_conjecture/rk31uUHv">Hodge conjecture</a>. </p>