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The Hodge Conjecture

On a nonsingular complex projective variety, every rational Hodge class is a rational combination of classes of algebraic cycles.

1 statement · 0 links from papers · 0 composed · updated 2026-08-12 14:30:23.227138+00:00

Typed form: /api/frontier/hodge-conjecture · the inclusive shelf of every claim is at /topics/hodge-conjecture

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Derived, and unstated

Each of these follows from links two or more papers assert, but no paper in the corpus states it. A chain is only as strong as its weakest link, and the tier below reports that weakest link, not the best one.

  1. Nothing composes yet. That happens when the recorded links do not yet chain: a new paper reducing something to one of the classical criteria below is what starts it.

What would settle it

  1. No routes recorded yet.

What it would settle

  1. No consequences recorded yet.