Logarithmic geometry and Frobenius
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909185284767744 |
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| author | Kato, Kazuya Nakayama, Chikara Usui, Sampei |
| author_facet | Kato, Kazuya Nakayama, Chikara Usui, Sampei |
| contents | Based on the logarithmic algebraic geometry and the theory of Deligne systems, we define an abelian category of $\ell$-adic sheaves with weight filtrations on a logarithmic scheme over a finite field, which is similar to the category of variations of mixed Hodge structure. We consider asymptotic behaviors and simple cases of higher direct images of objects of this category. This category is closely related to the monodromy-weight conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_19183 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Logarithmic geometry and Frobenius Kato, Kazuya Nakayama, Chikara Usui, Sampei Algebraic Geometry Primary 14A21, Secondary 14F06, 14G15 Based on the logarithmic algebraic geometry and the theory of Deligne systems, we define an abelian category of $\ell$-adic sheaves with weight filtrations on a logarithmic scheme over a finite field, which is similar to the category of variations of mixed Hodge structure. We consider asymptotic behaviors and simple cases of higher direct images of objects of this category. This category is closely related to the monodromy-weight conjecture. |
| title | Logarithmic geometry and Frobenius |
| topic | Algebraic Geometry Primary 14A21, Secondary 14F06, 14G15 |
| url | https://arxiv.org/abs/2404.19183 |