Bounding crystalline torsion from étale torsion
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866916796010856448 |
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| author | Gabber, Ofer Li, Shizhang |
| author_facet | Gabber, Ofer Li, Shizhang |
| contents | In this note, we prove that given a smooth proper family over a $p$-adic ring of integers, one gets a control of its crystalline torsion in terms of its étale torsion, the cohomological degree, and the ramification. Our technical core result is a boundedness result concerning annihilator ideals of $u^{\infty}$-torsion in Breuil--Kisin prismatic cohomology, which might be of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_13543 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bounding crystalline torsion from étale torsion Gabber, Ofer Li, Shizhang Algebraic Geometry Number Theory In this note, we prove that given a smooth proper family over a $p$-adic ring of integers, one gets a control of its crystalline torsion in terms of its étale torsion, the cohomological degree, and the ramification. Our technical core result is a boundedness result concerning annihilator ideals of $u^{\infty}$-torsion in Breuil--Kisin prismatic cohomology, which might be of independent interest. |
| title | Bounding crystalline torsion from étale torsion |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2506.13543 |