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The rational Hodge conjecture for CM abelian varieties

Hodge classes are cohomological objects; the problem asks whether rational ones come from algebraic cycles on abelian varieties with complex multiplication.

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Understanding the problem

Read the background

Hodge classes are cohomological objects; the problem asks whether rational ones come from algebraic cycles on abelian varieties with complex multiplication.

Why it matters

A precise target for comparing mathematical claims, their baselines, and the documented contribution of AI.

What counts as progress

A sourced theorem, construction, algorithm, bound, or substantive formalization with its assumptions and AI role stated.

What to watch for

  • Check the exact hypotheses and compare with the stated prior baseline.
  • Distinguish a source claim, an available proof, and a reproduced verification.
  • Retain human contributions, competing work, corrections, and withdrawals.

Background review: 2026-10-11. Selected sources:

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