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The suspicion of Hodge is an important unresolved problem in algebraic geometry, which relates the algebraic topology of a non-singular complex algebraic variety and the varieties of this variety to each other. More specifically, it is suspected that certain Rham cohomology classes are algebraic, that is, they are sums of Poincaré duals of the homology classes of sub-variables. The suspicion of Hodge is one of seven $ 1,000,000 Millennium Prize Issues promised by the Clay Mathematics Institute for anyone who proves Hodge's suspicion.
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