Some Foundational Results In Adic Geometry
Algebraic Geometry
2025-07-21 v2
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.
Cite
@article{arxiv.2409.15516,
title = {Some Foundational Results In Adic Geometry},
author = {Bogdan Zavyalov},
journal= {arXiv preprint arXiv:2409.15516},
year = {2025}
}
Comments
Updated Version. Comments are very welcome! A previous version of the paper appeared before here https://bogdanzavyalov.com/refs/notes/adic_notes.pdf