If solved
Algebraic Cycles Understood
A proof would link the topology of algebraic varieties to the shapes that polynomial equations can cut out.
Open in the interactive tree →Knowing which cohomology classes come from algebraic cycles would give algebraic geometry a bridge between analysis, topology and algebra. It would also support work on related conjectures such as the Tate conjecture.
What it brings
- A topological test for which subvarieties exist
- Progress on the Tate conjecture
- Firmer foundations for the theory linking cohomology and cycles
Prerequisites
- Topology1895Algebraic cycles are studied through topological invariants
- Hodge Conjectureopen