Dagger geometry as Banach algebraic geometry
Copyright policy )Dagger geometry as Banach algebraic geometry
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-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). 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.
- THE CHANCELLOR, MASTERS AND SCHOLARS OF THE UNIVERSITY OF OXFORD United Kingdom
- University of Padua Italy
- University of Regensburg Germany
Mathematics - Number Theory, Analytical algebras and rings, Generalizations (algebraic spaces, stacks), Rigid analytic geometry, Functional Analysis (math.FA), rigid geometry, Mathematics - Functional Analysis, global analytic geometry, Mathematics - Algebraic Geometry, 14A20, 13J07, 14G22, 14E25, 46M99, 18D10, 19D23, 14F20, Global analytic geometry; Over-convergent structure sheaf; Rigid geometry, Monoidal, symmetric monoidal and braided categories, FOS: Mathematics, over-convergent structure sheaf, Number Theory (math.NT), Embeddings in algebraic geometry, Algebraic Geometry (math.AG)
Mathematics - Number Theory, Analytical algebras and rings, Generalizations (algebraic spaces, stacks), Rigid analytic geometry, Functional Analysis (math.FA), rigid geometry, Mathematics - Functional Analysis, global analytic geometry, Mathematics - Algebraic Geometry, 14A20, 13J07, 14G22, 14E25, 46M99, 18D10, 19D23, 14F20, Global analytic geometry; Over-convergent structure sheaf; Rigid geometry, Monoidal, symmetric monoidal and braided categories, FOS: Mathematics, over-convergent structure sheaf, Number Theory (math.NT), Embeddings in algebraic geometry, Algebraic Geometry (math.AG)
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