Hodge conjecture.
“Who doesn’t like complex algebraic problems”, if one were a math obsessed, he would definitely say this. Well if you are one such obsessive mathematician, then here is an algebraic equation that might keep you busy for a long time, a long time. Statement: Let X be a non-singular complex projective manifold. Then every Hodge class on X is a linear combination with rational coefficients of the co-homology classes of complex sub-varieties of X.
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“Who doesn’t like complex algebraic problems”, if one were a math obsessed, he would definitely say this. Well if you are one such obsessive mathematician, then here is an algebraic equation that might keep you busy for a long time, a long time. Statement: Let X be a non-singular complex projective manifold. Then every Hodge class on X is a linear combination with rational coefficients of the co-homology classes of complex sub-varieties of X.