trailThe separable Jacobian conjecture is false in dimension two in characteristic two.
Every polynomial map of ℂ² with nonzero constant Jacobian determinant has a polynomial inverse
Mondello's counterexample to the two-dimensional separable Jacobian conjecture in characteristic two is correct.
Mondello's plane map (P,Q) over the algebraic closure of F₂ has Jacobian determinant 1 and generic degree 3 yet is not injective.
In positive characteristic the Jacobian conjecture is standardly formulated as: étale polynomial self-maps of affine space with generic degree prime to the characteristic are automorphisms.
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The separable Jacobian conjecture is false in dimension three in characteristic two.
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The separable Jacobian conjecture is false in dimension two in characteristic two.
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