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Huneke-Wiegand Conjecture

Algebra · posed by Craig Huneke & Roger Wiegand, 1994 · disproved

2 comments

Statement

The Huneke–Wiegand Conjecture: Let RR be a one-dimensional Gorenstein local domain, and let MM be a finitely generated, non-zero, torsion-free RR-module. If the tensor product M⊗RM∗M \otimes_R M^* is torsion-free, then MM is a projective (hence free) RR-module.

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No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. construction · #1

    GPT-5.6-Pro, with Son Pham & Craig Huneke

    The record says a model found this and names the people who worked on it. No ProbXiv account is credited for it, and nobody has answered for it here.

    AI involvement
    ai discovered
    — the result was found by a model.

    Came up with the counterexample on shot. GPT-share chat for proof:

    https://chatgpt.com/c/6a6529a6-fb04-83ea-a397-a64ffed0b3d6

    Verified by author of the conjecture

  2. Recorded elsewhere on #1 · not checked here

    recorded: correctVibeMathed expert verification (imported)

    scope Expert review reported upstream; the reviewer has no probXiv account and is not credited here

    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

    Repeated from the source; nothing was checked here.

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