Cohomologically smooth morphisms for \'etale $\mathbb F_p$-sheaves in characteristic $p$

Felix Lotter

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arXiv · 2403.11149

Cohomologically smooth morphisms for \'etale $\mathbb F_p$-sheaves in characteristic $p$

Felix Lotter

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Abstract

We scrutinise the notions of cohomologically smooth morphisms and smooth objects for the six functor formalism of \'etale $\mathbb F_p$-sheaves on schemes in characteristic $p$. We show that only cohomologically \'etale morphisms are cohomologically smooth in this setting. This is complemented by a characterisation of cohomologically \'etale morphisms in arbitrary characteristic. In fact, we prove that such a morphism is already \'etale up to universal homeomorphism.

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Felix Lotter. 2024-03-17. Cohomologically smooth morphisms for \'etale $\mathbb F_p$-sheaves in characteristic $p$. https://arxiv.org/abs/2403.11149

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