The Separable Jacobian Conjecture in Characteristic 2
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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.
Context
the counterexample to the original Jacobian conjecture does not specialize to characteristic 2; this is a modification that does
The separable formulation is the version of the Jacobian conjecture designed to survive in positive characteristic, and the author notes no other counterexample to it is known.
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the counterexample to the original Jacobian conjecture does not specialize to characteristic 2; this is a modification that does
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Machine check · not human verification
machine: correctscope 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 Single-author arXiv note, not yet peer-reviewed.
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