algebra / Affine algebraic geometry
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 $F: \mathbb{A}_k^3 \to \mathbb{A}_k^3$ over any field of characteristic $2$ has Jacobian determinant identically $1$ and function-field degree $3$, yet is not injective.
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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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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 $F: \mathbb{A}_k^3 \to \mathbb{A}_k^3$ over any field of characteristic $2$ has Jacobian determinant identically $1$ and function-field degree $3$, yet is not injective.
the counterexample to the original Jacobian conjecture does not specialize to characteristic 2; this is a modification that does
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