Topological rigidity of maps in positive characteristic and anabelian geometry

Author:

Piotr Achinger, Jakob Stix

Keyword:

Mathematics, Algebraic Geometry, Algebraic Geometry (math.AG), Number Theory (math.NT)

journal:

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date:

2023-10-16 16:00:00

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 \'etale fundamental groups. We extend Tamagawa's result by adding a purely topological criterion for maps to agree up to a power of Frobenius.