Logarithmic Tate conjectures over finite fields
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866913705010135040 |
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| author | Kato, Kazuya Nakayama, Chikara Usui, Sampei |
| author_facet | Kato, Kazuya Nakayama, Chikara Usui, Sampei |
| contents | We formulate an analogue of Tate conjecture on algebraic cycles, for the log geometry over a finite field. We show that the weight-monodromy conjecture follows from this conjecture and from the semi-simplicity of the Frobenius action. This conjecture suggests the existence of the monodromy cycle which gives the monodromy operator and an action of ${\frak{sl}}(2)$ on the cohomology, and which lives in the world of log motives. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_16974 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Logarithmic Tate conjectures over finite fields Kato, Kazuya Nakayama, Chikara Usui, Sampei Algebraic Geometry Primary 14A21, Secondary 14F20, 19E15 We formulate an analogue of Tate conjecture on algebraic cycles, for the log geometry over a finite field. We show that the weight-monodromy conjecture follows from this conjecture and from the semi-simplicity of the Frobenius action. This conjecture suggests the existence of the monodromy cycle which gives the monodromy operator and an action of ${\frak{sl}}(2)$ on the cohomology, and which lives in the world of log motives. |
| title | Logarithmic Tate conjectures over finite fields |
| topic | Algebraic Geometry Primary 14A21, Secondary 14F20, 19E15 |
| url | https://arxiv.org/abs/2502.16974 |