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arXiv · 2002.11608

Fr\'echet Modules and Descent

Oren Ben-Bassat·Kobi Kremnizer
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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 Fr\'{e}chet 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.

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BibTeXRIS

Oren Ben-Bassat, Kobi Kremnizer. 2020-02-26. Fr\'echet Modules and Descent. https://doi.org/10.70930/tac/reiq1jwu

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