Some Foundational Results In Adic Geometry

Bogdan Zavyalov

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arXiv · 2409.15516

Some Foundational Results In Adic Geometry

Bogdan Zavyalov

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Abstract

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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Bogdan Zavyalov. 2024-09-23. Some Foundational Results In Adic Geometry. https://arxiv.org/abs/2409.15516

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