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Open-problem statements, with their sources attached.

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Open problemEditorial · Algebraic geometry

Hodge Conjecture

On a smooth projective complex variety, every rational Hodge class of type (p,p)(p,p) is a rational linear combination of classes of algebraic cycles.

Source checked Jul 24, 20261 pinned Lean statementInspect problem
Open problemEditorial · Geometry and topology

Inscribed Square Problem

Every Jordan curve γ:S1R2\gamma:S^1\to\mathbb{R}^2 contains four points that are the vertices of a nondegenerate square.

Source checked Jul 24, 20261 pinned Lean statementInspect problem