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arXiv · 1502.01401

Dagger Geometry As Banach Algebraic Geometry

Federico Bambozzi·Oren Ben-Bassat
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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.

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Federico Bambozzi, Oren Ben-Bassat. 2015-02-05. Dagger Geometry As Banach Algebraic Geometry. https://doi.org/10.1016/j.jnt.2015.10.023

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