The Separable Jacobian Conjecture in Characteristic 2
Statement
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.
Record
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No person has examined this. Nothing here has been checked at all. say whether it holds →
construction · #1
Irit Huq-Kuruvilla, using ChatGPT 5.6 SolThat credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.
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.
the counterexample to the original Jacobian conjecture does not specialize to characteristic 2; this is a modification that does
Recorded elsewhere on #1 · not checked here
recorded: correctVibeMathed site checkscope Reproduction by the VibeMathed site
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 Single-author arXiv note, not yet peer-reviewed.
Repeated from the source; nothing was checked here.
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