Beilinson-Parshin adeles via solid algebraic geometry
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866908468802224128 |
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| author | Brav, Christopher Konovalov, Grigorii |
| author_facet | Brav, Christopher Konovalov, Grigorii |
| contents | In this paper, we apply Clausen-Scholze's theory of solid modules to the existence of adelic decompositions for schemes of finite type over $\mathbb{Z}$. Specifically, we use the six-functor formalism for solid modules to define the skeletal filtration of a scheme, and then we show that decomposing a quasi-coherent sheaf with respect to this filtration gives rise to a new construction of the Beilinson-Parshin adelic resolution. As an application of the adelic decomposition combined with some nice completeness properties of the solid tensor product, we prove a version of adelic descent for solid quasi-coherent sheaves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_08472 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Beilinson-Parshin adeles via solid algebraic geometry Brav, Christopher Konovalov, Grigorii Algebraic Geometry In this paper, we apply Clausen-Scholze's theory of solid modules to the existence of adelic decompositions for schemes of finite type over $\mathbb{Z}$. Specifically, we use the six-functor formalism for solid modules to define the skeletal filtration of a scheme, and then we show that decomposing a quasi-coherent sheaf with respect to this filtration gives rise to a new construction of the Beilinson-Parshin adelic resolution. As an application of the adelic decomposition combined with some nice completeness properties of the solid tensor product, we prove a version of adelic descent for solid quasi-coherent sheaves. |
| title | Beilinson-Parshin adeles via solid algebraic geometry |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2403.08472 |