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Some Foundational Results In Adic Geometry

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arxiv 2409.15516 v2 pith:DXWKA6MX submitted 2024-09-23 math.AG

Bogdan Zavyalov This is my paper · ORCID
classification math.AG
keywords adicgeometryresultsanalyticcontextdevelopfoundationalsome
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In this paper, we record some foundational results on adic geometry that seem to be missing in the existing literature. Namely, we develop the Proj construction and a theory of lci closed immersions in the context of locally noetherian analytic adic spaces. In the context of rigid-analytic spaces, these topics have previously been considered in [GL21] and [Con07]. We also develop an etale six functor formalism in the analytic geometry and give a categorical description of lisse and constructible sheaves. All results of this paper are probably well-known to the experts.

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Cited by 1 Pith paper

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  1. Vanishing Cycles for Zariski-Constructible Sheaves on Rigid Analytic Varieties

    math.AG 2025-04 accept novelty 7.0 of 10

    Nearby and vanishing cycle functors on rigid analytic varieties preserve Zariski-constructibility, satisfy Beilinson gluing, are perverse t-exact, and commute with Verdier duality.

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