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arXiv · 2310.11591

Topological rigidity of maps in positive characteristic and anabelian geometry

Piotr Achinger·Jakob Stix
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Abstract

We study pairs of non-constant maps between two integral schemes of finite type over two (possibly different) fields of positive characteristic. When the target is quasi-affine, Tamagawa showed that the two maps are equal up to a power of Frobenius if and only if they induce the same homomorphism on their étale fundamental groups. We extend Tamagawa's result by adding a purely topological criterion for maps to agree up to a power of Frobenius.

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Piotr Achinger, Jakob Stix. 2023-10-17. Topological rigidity of maps in positive characteristic and anabelian geometry. https://arxiv.org/abs/2310.11591

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