Fréchet Modules and Descent

Abstract

We study several aspects of the study of Ind-Banach modules over Banach rings thereby synthesizing some aspects of homological algebra and functional analysis. This includes a study of nuclear modules and of modules which are flat with respect to the projective tensor product. We also study metrizable and Fréchet Ind-Banach modules. We give explicit descriptions of projective limits of Banach rings as ind-objects. We study exactness properties of projective tensor product with respect to kernels and countable products. As applications, we describe a theory of quasi-coherent modules in Banach algebraic geometry. We prove descent theorems for quasi-coherent modules in various analytic and arithmetic contexts.

arXiv commentimproved version

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Cited by in corpus (6)

• Analytic geometry over F_1 and the Fargues-Fontaine curve
• On the Sheafyness Property of Spectra of Banach Rings
• Period Rings with Big Coefficients and Application II
• Analytification, localization and homotopy epimorphisms
• Derived Analytic Geometry for Z-Valued Functions. Part I -- Topological Properties
• Six operations for D-cap-modules on rigid analytic spaces