The Hodge conjecture asserts that, for particularly nice types of spaces called projective algebraic varieties, the pieces called Hodge cycles are actually rational linear combinations of geometric pieces called algebraic cycles.
Hodge Conjecture
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References
Clay Mathematics Institute. "Hodge Conjecture." http://www.claymath.org/millennium/Hodge_Conjecture/.Deligne, P. "The Hodge Conjecture." http://www.claymath.org/millennium/Hodge_Conjecture/Official_Problem_Description.pdf.Grothendieck, A. "Hodge's General Conjecture Is False for Trivial Reasons." Topology 8, 299-303, 1969.Hodge, W. V. D. "The Topological Invariants of Algebraic Varieties." Proc. Internat. Congress Math., Cambridge, Mass., 1950, Vol. 1. Providence, RI: Amer. Math. Soc., pp. 182-192, 1952.Referenced on Wolfram|Alpha
Hodge ConjectureCite this as:
Weisstein, Eric W. "Hodge Conjecture." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HodgeConjecture.html