Local Cohomology Modules With Nonclosed Support
Can a noetherian ring have a local cohomology module whose support is not closed - equivalently, one with infinitely many minimal primes? Huneke and Lyubeznik asked; the paper constructs such rings, so the answer is yes.
- Result
- Proved
- Status
- Resolved
- AI contribution
- AI co-developed
- Method
- Construction
- Field
- Commutative Algebra, Local Cohomology
- Posed by
- Craig Huneke and Gennady Lyubeznik
- Year posed
- —
- Years open
- —
- Solved
- 2026-07-30
- Model
- ChatGPT 5.5 / 5.6
- Vendor
- OpenAI
- Collaborators
- Bhargav Bhatt, Linquan Ma
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 25 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
Per the paper's AI disclosure, the examples arose through interactions with ChatGPT 5.5 and 5.6. The model's first attempt at Question 1.1 was flawed but carried the idea of using torsion points on elliptic curves; pushed further, it produced a counterexample, which the authors modified and simplified into the normal example of Theorem 2.4. In a separate interaction the model found the example behind Theorem 1.3. The authors wrote the paper with Codex assistance and take responsibility for correctness.
Verification
No independent check. The authors state plainly that they are responsible for correctness, and the disclosure records that the model's first proposed solution was wrong before a usable idea emerged. Preprint, not refereed.