PPL 088 / 177 permanent IDsPrize Problem Ledger · PPLChecked 2026.07.26
Permanent problem IDPPL 088
Verified openInstitutionalconjecture
Algebraic geometry
Hodge conjecture
On a smooth projective complex algebraic variety, every rational Hodge class should be a rational linear combination of classes of algebraic cycles.
topologyalgebraic cyclescomplex geometry
01
The problem
On a smooth projective complex algebraic variety, every rational Hodge class should be a rational linear combination of classes of algebraic cycles.
Open since1950exact
Last checked2026.07.26Catalog verification
02
Reward offers
Offer 01$1,000,000Clay Mathematics Institute
InstitutionalClay does not accept direct submissions. A proposed solution must be published in a qualifying outlet, at least two years must pass, and the work must gain general acceptance in the mathematics community while resolving the complete official formulation.