Baker's Question on Smooth Hyperplane Sections over Finite Fields
Baker asked, as recorded by Poonen, whether a fixed smooth quasiprojective variety over a finite field must acquire a smooth rational hyperplane section after every sufficiently high-dimensional linearly nondegenerate embedding. Poonen predicted no for every positive-dimensional variety, and that prediction is correct.
- Result
- Disproved
- Status
- Resolved
- AI contribution
- AI-assisted
- Method
- Construction
- Field
- Algebraic geometry
- Posed by
- Matthew Baker; prediction by Bjorn Poonen
- Year posed
- —
- Years open
- —
- Solved
- 2026-06-22
- Model
- GPT-based models, Rethlas
- Vendor
- OpenAI / Frenzy Math
- Collaborators
- Yutong Zhang, Yaoran Yang
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 15 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
The acknowledgement says the author used GPT-based large language models to generate and compare possible proof strategies, some of which was incorporated into the final manuscript, and used the Rethlas agent as an auxiliary proof-checker.
Verification
arXiv preprint; not yet peer-reviewed.
Source
arXiv:2606.23513 - Hyperplane anti-Bertini embeddings over finite fields