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arXiv · 2606.15429

When is Frobenius epic?

Javier Carvajal-Rojas·Rankeya Datta·Noah Olander·Axel Stäbler
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Abstract

We prove that a homomorphism of rings of prime characteristic is b-nil formally unramified if and only if its relative Frobenius is an epimorphism. We specialize this result under different finiteness conditions such as (relative) $F$-finiteness and Noetherianity. We give an example where the absolute Frobenius is an epimorphism but is not surjective, as well as an example of a formally unramified homomorphism that is not b-nil formally unramified.

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Javier Carvajal-Rojas, Rankeya Datta, Noah Olander, Axel Stäbler. 2026-06-13. When is Frobenius epic?. https://arxiv.org/abs/2606.15429

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