Fréchet Modules and Descent
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2020
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866908886398664704 |
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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 |