Slopes and weights of $\ell$-adic cohomology of rigid spaces
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_ | 1866913775933718528 |
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| author | Lu, Qing Zheng, Weizhe |
| author_facet | Lu, Qing Zheng, Weizhe |
| contents | We prove that Frobenius eigenvalues of $\ell$-adic cohomology and $\ell$-adic intersection cohomology of rigid spaces over $p$-adic local fields are algebraic integers and we give bounds for their $p$-adic valuations. As an application, we deduce bounds for their weights, proving conjectures of Bhatt, Hansen, and Zavyalov. We also give examples of monodromy-pure perverse sheaves on projective curves with non monodromy-pure cohomology, answering a question of Hansen and Zavyalov. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_05421 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Slopes and weights of $\ell$-adic cohomology of rigid spaces Lu, Qing Zheng, Weizhe Algebraic Geometry Number Theory 14F20, 14G22 We prove that Frobenius eigenvalues of $\ell$-adic cohomology and $\ell$-adic intersection cohomology of rigid spaces over $p$-adic local fields are algebraic integers and we give bounds for their $p$-adic valuations. As an application, we deduce bounds for their weights, proving conjectures of Bhatt, Hansen, and Zavyalov. We also give examples of monodromy-pure perverse sheaves on projective curves with non monodromy-pure cohomology, answering a question of Hansen and Zavyalov. |
| title | Slopes and weights of $\ell$-adic cohomology of rigid spaces |
| topic | Algebraic Geometry Number Theory 14F20, 14G22 |
| url | https://arxiv.org/abs/2502.05421 |