Local Cohomology Modules With Nonclosed Support
Statement
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.
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construction · #1
Bhargav Bhatt and Linquan Ma, using ChatGPT 5.5, 5.6That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.
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.
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