Huneke-Wiegand Conjecture
The Huneke–Wiegand Conjecture: Let be a one-dimensional Gorenstein local domain, and let be a finitely generated, non-zero, torsion-free -module. If the tensor product is torsion-free, then is a projective (hence free) -module.
- Result
- Disproved (Verified by author of the conjecture)
- Status
- Resolved
- AI contribution
- AI-discovered
- Method
- Construction
- Field
- Commutative Algebra
- Posed by
- Craig Huneke & Roger Wiegand
- Year posed
- 1994
- Years open
- 32y
- Solved
- 2026-07-29
- Model
- GPT-5.6-Pro
- Vendor
- —
- Collaborators
- Craig Huneke
- Verification
- Independently expert-verified
- Publication
- Announced
- Significance
- 20 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
Came up with the counterexample on shot. GPT-share chat for proof: https://chatgpt.com/c/6a6529a6-fb04-83ea-a397-a64ffed0b3d6
Verification
The proposed data are: Γ = ⟨56,57,58,63,64,70,71,72,73,74,75,76,77,78,79,80,81,82,83, 87,89,90,93,95,96,97⟩, R = ℚ[t^Γ]_𝔪 I = (t^56,t^70)R Full link: https://github.com/sonpham-org/huneke-wiegand-candidate-verification Contains my own counter example proof and an independent verification by the conjecture author
Source
Submitted by HiddenLemur412