Hodge conjecture
Is every Hodge class on a projective variety a combination of algebraic cycles?
Summary
Asks whether certain cohomology classes on smooth complex projective varieties can always be built from algebraic subvarieties.
Source
Open, as listed by Clay Mathematics Institute · Millennium Prize Problems. Checked 29 Sep 2026.
The status is the source’s. Papex does not decide whether a problem is solved.
Prize
Clay Mathematics Institute · $1,000,000
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