The Separable Jacobian Conjecture in Characteristic 2
Adjamagbo's positive-characteristic refinement of the Jacobian conjecture asks that a polynomial endomorphism with unit Jacobian determinant whose induced function-field extension has degree prime to the characteristic be an automorphism. It is false: an explicit over any field of characteristic has Jacobian determinant identically and function-field degree , yet is not injective.
- Result
- Disproved(see note)
- Status
- Resolved
- AI contribution
- AI co-developed
- Method
- Construction
- Field
- Affine algebraic geometry
- Posed by
- Pascal Adjamagbo
- Year posed
- —
- Years open
- —
- Solved
- 2026-07-23
- Model
- ChatGPT 5.6 Sol
- Vendor
- OpenAI
- Collaborators
- Irit Huq-Kuruvilla
- Verification
- Site-confirmed
- Publication
- Preprint
- Significance
- 25 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What was actually shown
the counterexample to the original Jacobian conjecture does not specialize to characteristic 2; this is a modification that does
What the AI did
The AI usage section states that the text is the result of a discussion with ChatGPT 5.6 Sol, with conversation transcripts available on request, and that the proof itself was verified as correct by the named author.
Verification
The counterexample is a three-line explicit polynomial map; the non-injectivity is witnessed by three distinct source points and the Jacobian determinant is a direct computation, both checkable by hand. Single-author arXiv note, not yet peer-reviewed.
Source
arXiv:2607.20968 - An Explicit Characteristic-2 Counterexample to the Separable Jacobian Conjecture