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Hodge conjecture

Category: Mathematics

Status: Queued

The Hodge conjecture asks whether certain de Rham cohomology classes on a non-singular complex projective variety are algebraic — that is, rational combinations of cohomology classes of algebraic subvarieties.

It is a Millennium Prize problem linking algebraic geometry and differential geometry. The conjecture is known to hold in several special cases but the general statement is wide open.

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