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arXiv · 2101.09759

The six functors for Zariski-constructible sheaves in rigid geometry

Bhargav Bhatt·David Hansen
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Abstract

We prove a generic smoothness result in rigid analytic geometry over a characteristic zero nonarchimedean field. The proof relies on a novel notion of generic points in rigid analytic geometry which are well-adapted to "spreading out" arguments, in analogy with the use of generic points in scheme theory. As an application, we develop a six functor formalism for Zariski-constructible \'etale sheaves on characteristic zero rigid spaces. Among other things, this implies that characteristic zero rigid spaces support a well-behaved theory of perverse sheaves.

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Bhargav Bhatt, David Hansen. 2021-01-24. The six functors for Zariski-constructible sheaves in rigid geometry. https://arxiv.org/abs/2101.09759

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