Problem detail · source-aware
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For a Brauer class on a variety, the period-index conjecture bounds the index in terms of the period and the dimension. Disproved: for any uncountable algebraically closed field $k$ of characteristic $0$ and any $d \geq 3$ there is a $d$-dimensional variety over $k$ carrying a Brauer class that violates it, for Hodge-theoretic reasons. For $d = 3$ the construction needs no uncountability, so the conjecture fails already over $\overline{\mathbf{Q}}$.
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The paper's AI disclosure is unusually specific about a partial success. Prompted to find a counterexample by the Hodge-theoretic strategy, ChatGPT produced an example that was flawed, but whose shape survived into the final solution: a quotient of the same form, with an abelian surface, a genus two curve and the group Z/4. The author refined that into the working construction.
Provider: OpenAI · Prompt public: unknown · Independence: unknown
arXiv preprint, not yet peer-reviewed.
Correctness: unknown · statement fidelity: unaudited · peer review: none
VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Source-reported tools: construction.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.