Answer by Francesco Minnocci for Strengthening Ax-Grothendieck
A version of OP's claim (with an additional hypothesis) is mentioned in a footnote on the first page ofBorel, A. Injective endomorphisms of algebraic varieties. Arch. Math 20, 531–537 (1969)....
View ArticleAnswer by pinaki for Strengthening Ax-Grothendieck
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...
View ArticleAnswer by Jason Starr for Strengthening Ax-Grothendieck
Edit. To try and make something productive out of the argument below, let me explain the proof of the Ax-Grothendieck Theorem for affine space using this argument. Also, the argument below includes the...
View ArticleStrengthening Ax-Grothendieck
The question was cross-posted from Math.SE: https://math.stackexchange.com/questions/4566017/strengthening-ax-grothendieckThe question is simple. The Ax-Grothendieck theorem says a polynomial map...
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