Proposed
Proposed source assertion awaiting assessment ↗
Only the cited assertion with its exact assumptions. This report does not resolve the canonical Problem or establish independent OpenMath mathematical review.
Observed Oct 10, 2026
Theorem · version 1
Proposed Hodge result for all CM abelian varieties
Earlier version 1. View current version 2 →
Statement
For every complex CM abelian variety A and every p ≥ 0, CH^p(A)⊗Q → H^{2p}(A,Q) ∩ H^{p,p}(A) is surjective. The provider includes all finite products and powers of CM abelian varieties.
Assumptions
- Complex abelian variety of CM type: End(A)⊗Q contains a commutative semisimple Q-algebra of dimension 2 dim A.
- Rational cycle classes; every codimension.
Scope
Provider proposal for a specified family in arbitrary dimension; not rational Hodge for every smooth projective variety.
This source presents a theorem with a proposed proof. Its wording does not establish acceptance or independent mathematical review.
Evidence
Source reports
Connections
In this problem · publication v6 · Selected context
Hodge conjecture →
Special case · Proposed
Relationship not independently reviewed. This concerns its use in this problem.
In this problem · publication v8
Hodge conjecture →
Special case · Proposed
Relationship not independently reviewed. This concerns its use in this problem.
Sources
OpenAI · proposed Hodge theorem for CM abelian varieties →
- Theorem 1.1 and definition of CM type, PDF page 1 → · Original passage ↗
Recorded wording
The provider claims rational Hodge for every complex CM abelian variety in all dimensions and codimensions, including finite products and powers.
paraphrase · Only metadata and original OpenMath paraphrases are published; full text stays upstream.
OpenAI · Preprint · Publication date Oct 6, 2026
Provider preprint in the October 2026 public collection. The selected manuscript is a proposal here; a release announcement is not independent expert acceptance.
OpenAI · proposed Hodge theorem for CM abelian varieties — manuscript ↗No OpenMath execution recorded
Revision & attribution
Source revision: fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb. Observed Oct 10, 2026.
The provider attributes this manuscript to its internal AI model. Mathematical acceptance, paper-to-formal correspondence and independent reproduction are not established by OpenMath.
OpenAI · proposed Hodge theorem for CM abelian varieties — manuscript: fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb. External manuscript. No OpenMath proof execution, formalization or independent mathematical acceptance is inferred.
History
Statement versions
Statement versions and problem publication versions are separate. A new publication can update context or sources while retaining the same statement.
Assessment history · 1
Assessments retained in these publication records. Earlier statement versions retain their own source histories.
Proposed
Proposed source assertion awaiting assessment ↗
Only the cited assertion with its exact assumptions. This report does not resolve the canonical Problem or establish independent OpenMath mathematical review.
Observed Oct 10, 2026 · Source passage →
Record details
- Claim ID
- claim-hodge-openai-cm-proposal
- Statement version
- 1
- SHA-256
- 8900e061af14fb295b9421a8ab3f56e3b2d02790c08336ffc119dbb1bbfa7903