In this article, we look at analytic geometry from the perspective of relative algebraic geometry with respect to the categories of bornological and Ind-Banach spaces over valued fields (both Archimedean and non-Archimedean). We are able to recast the theory of Grosse-Klönne 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) and for the condition of a family of morphisms to be a cover. 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.

Dagger geometry as Banach algebraic geometry

Bambozzi F.;
2016

Abstract

In this article, we look at analytic geometry from the perspective of relative algebraic geometry with respect to the categories of bornological and Ind-Banach spaces over valued fields (both Archimedean and non-Archimedean). We are able to recast the theory of Grosse-Klönne 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) and for the condition of a family of morphisms to be a cover. 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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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/3477975
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