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| Главные авторы: | , |
|---|---|
| Формат: | Preprint |
| Опубликовано: |
2020
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| Предметы: | |
| Online-ссылка: | https://arxiv.org/abs/2002.11608 |
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Оглавление:
- 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.