Fréchet Modules and Descent

Fuente: arXiv
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Autores principales: Ben-Bassat, Oren, Kremnizer, Kobi
Formato: Preprint
Publicado: 2020
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author Ben-Bassat, Oren
Kremnizer, Kobi
author_facet Ben-Bassat, Oren
Kremnizer, Kobi
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2002_11608
institution arXiv
publishDate 2020
record_format arxiv
spellingShingle Fréchet Modules and Descent
Ben-Bassat, Oren
Kremnizer, Kobi
Functional Analysis
Algebraic Geometry
Category Theory
Complex Variables
Number Theory
math.AG, math.CT, math.RT, math.NT, math.FA
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.
title Fréchet Modules and Descent
topic Functional Analysis
Algebraic Geometry
Category Theory
Complex Variables
Number Theory
math.AG, math.CT, math.RT, math.NT, math.FA
url https://arxiv.org/abs/2002.11608