Dagger Geometry As Banach Algebraic Geometry
Algebraic Geometry
2022-10-12 v2 Functional Analysis
Number Theory
Abstract
In this article, we apply the approach of relative algebraic geometry towards analytic geometry to the category of bornological and Ind-Banach spaces (non-Archimedean or not). We are able to recast the theory of Grosse-Kl\"onne dagger affinoid domains with their weak G-topology in this new language. We prove an abstract recognition principle for the generators of their standard topology (the morphisms appearing in the covers). We end with a sketch of an emerging theory of dagger affinoid spaces over the integers, or any Banach ring, where we can see the Archimedean and non-Archimedean worlds coming together.
Cite
@article{arxiv.1502.01401,
title = {Dagger Geometry As Banach Algebraic Geometry},
author = {Federico Bambozzi and Oren Ben-Bassat},
journal= {arXiv preprint arXiv:1502.01401},
year = {2022}
}