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arXiv · 2602.16168

Proof of Miyanishi's conjecture on endomorphisms of varieties

Supravat Sarkar
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Abstract

If $X$ is a quasi-projective variety over a field $k$ and $\phi$ a birational endomorphism of $X$ that is injective outside a closed subset of codimension $\geq 2$, we prove that $\phi$ is an automorphism. This generalizes an old theorem of Ax and proves a conjecture of Miyanishi. A key step in our proof is a finiteness result on class groups, which is of interest in its own right.

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Supravat Sarkar. 2026-02-18. Proof of Miyanishi's conjecture on endomorphisms of varieties. https://arxiv.org/abs/2602.16168

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