Theorem · version 1
Earlier version 1. View current version 2 →
Let A/Qbar have dimension d and good reduction A₀/Fpbar at a fixed p-adic place, and let γ be a rational Hodge class of degree 2r. For every list of d−r Cartier divisors on A₀, the trace of the specialized γ times their classes is a common q ∈ Q in every ℓ-adic realization (ℓ ≠ p) and in the specified de Rham–crystalline realization.
A provider proposal about rationality of pairings at one reduction place. Rationality alone is weaker than producing an algebraic representative for every complex Hodge class.
This source presents a theorem with a proposed proof. Its wording does not establish acceptance or independent mathematical review.
Proposed
Only the cited assertion with its exact assumptions. This report does not resolve the canonical Problem or establish independent OpenMath mathematical review.
OpenAI · proposed Milne rationality theorem · Theorem 1.1, PDF pages 1–2 →
Observed Oct 10, 2026
In this problem · publication v7 · Selected context
Different statement · related variant · Proposed
Relationship not independently reviewed. This concerns its use in this problem.
In this problem · publication v8
Different statement · related variant · Proposed
Relationship not independently reviewed. This concerns its use in this problem.
The provider claims that specialized rational Hodge classes pair with complementary products of divisors as one rational number in prime-to-p and crystalline realizations.
paraphrase · Only metadata and original OpenMath paraphrases are published; full text stays upstream.
OpenAI · Preprint · Publication date Oct 7, 2026
Provider preprint in the October 2026 public collection. The selected manuscript is a proposal here; a release announcement is not independent expert acceptance.
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 Milne rationality theorem — manuscript: fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb. External manuscript. No OpenMath proof execution, formalization or independent mathematical acceptance is inferred.
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Proposed
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 →