Bambozzi, Federico and Ben-Bassat, Oren (2016) Dagger geometry as Banach algebraic geometry. JOURNAL OF NUMBER THEORY, 162. pp. 391-462. ISSN 0022-314X, 1096-1658
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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-Klonne 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. (C) 2015 Elsevier Inc. All rights reserved.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | SPACES; Rigid geometry; Over-convergent structure sheaf; Global analytic geometry |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 01 Mar 2019 14:06 |
| Last Modified: | 05 Apr 2019 06:13 |
| URI: | https://pred.uni-regensburg.de/id/eprint/3050 |
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