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Answer by pinaki for Strengthening Ax-Grothendieck

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A counterexample for $n = 2$ is the map $(x_1, x_2) \mapsto (x_1x_2 - 1, x_2(x_1x_2 - 1) + x_1)$. This example, which I learned from a paper of Zbigniew Jelonek, was mentioned in an earlier answer of mine.


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