An Explicit Characteristic-2 Counterexample to the Separable Jacobian Conjecture

2026/07/23 by Irit Huq-Kuruvilla
#math.AG #math.AC

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Abstract

Let k be a field of characteristic 2. We exhibit an explicit polynomial endomorphism F: \mathbbA_k³→\mathbbA_k³ whose Jacobian determinant is identically 1, whose induced extension of rational function fields has degree 3, and which is nevertheless noninjective. Since 2≠ 3, this gives a counterexample to the usual Adjamagbo, or separable, formulation of the Jacobian conjecture in characteristic 2. Stabilization yields analogous counterexamples in every dimension n≥ 3

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