Limits RegistryPUBLIC RECORDLimits RegistryPUBLIC RECORDLimits RegistryPUBLIC RECORDLimits RegistryFor certain well-behaved geometric spaces called projective algebraic varieties, this asks whether every 'Hodge cycle' — a topological feature identified through the space's structure — can always be built out of actual algebraic (equation-defined) pieces. It is a question about how far topology and algebra can be identified with each other, central to how mathematicians reason about the shape of solution sets to polynomial equations.
The question, scope, and sources behind this Registry record.
On a non-singular complex projective algebraic variety, every Hodge class is a rational linear combination of classes of algebraic cycles.
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Current frontiers derived from accepted Claims.
The frontier is not sacred
Most progress starts with a disagreement that survives contact with evidence. If you can push the known lower bound up or pull the upper bound down, show us the work.
≥ when you have shown that at least this value is achievable.≤ when you have shown that anything above this value is impossible.No vibes. State the value, define the scope, and link the paper, proof, code, or reproduction that lets another person check it. Editors review every challenge before the public record changes.
Challenge this recordAssertions tied to evidence, attribution, and review.
No accepted Claims are recorded for this Limit yet.
The frontier as it changed over time.
Only accepted Claims matching the current specification contribute to the displayed bounds. Strict inequalities remain open; contradictory Claims require editorial review.