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Questions, not proof records

Open-problem statements, with their sources attached.

Each statement record keeps the mathematical question, a dated status source, accessible references, and any pinned Lean formulation separate from proof verification.

“Open” is a dated source assertion. In these pinned sources, sorry marks an admitted statement, not a proof. Source indexing does not mean the formulation has been independently built or certified by Therefore.
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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
Source labels openPapers · Algebraic geometry

Hartshorne Conjecture

There are no indecomposable vector bundles of rank 2 on Pn\mathbb{P}^n for n≥7n \ge 7. This is Conjecture 6.3 in [Har1974].

Source checked Jul 26, 20261 pinned Lean statementInspect problem
Source labels openWikipedia · Algebraic geometry

Jacobian conjecture

The Jacobian Conjecture: any regular function (i.e. vector valued polynomial function from) kⁿ → kᵐ whose Jacobian is a non-zero constant has an inverse that is given by a regular function, where k is a field of characteristic 0

Source checked Jul 26, 20261 pinned Lean statementInspect problem