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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.18763 |
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| _version_ | 1866914730709352448 |
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| author | Ren, Fei Rülling, Kay |
| author_facet | Ren, Fei Rülling, Kay |
| contents | Given an effective Cartier divisor D with simple normal crossing support on a smooth and proper scheme X over a perfect field of positive characteristic p, there is a natural notion of de Rham-Witt sheaves on X with zeros along D. We show that these sheaves correspond under Grothendieck duality for coherent sheaves to de Rham-Witt sheaves on X with modulus (X,D), as defined in the theory of cube invariant modulus sheaves with transfers developed by Kahn-Miyazaki-Saito-Yamazaki. From this we deduce refined versions of Ekedahl - and Poincaré duality for crystalline cohomology generalizing results of Mokrane and Nakkajima for reduced D, and a modulus version of Milne-Kato duality for étale motivic cohomology with p-primary torsion coefficients, which refines a result of Jannsen-Saito-Zhao. We furthermore get new integral models for rigid cohomology with compact supports on the complement of D and a modulus version of Milne's perfect Brauer group pairing for smooth projective surfaces over finite fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_18763 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Duality for Hodge-Witt cohomology with modulus Ren, Fei Rülling, Kay Algebraic Geometry Given an effective Cartier divisor D with simple normal crossing support on a smooth and proper scheme X over a perfect field of positive characteristic p, there is a natural notion of de Rham-Witt sheaves on X with zeros along D. We show that these sheaves correspond under Grothendieck duality for coherent sheaves to de Rham-Witt sheaves on X with modulus (X,D), as defined in the theory of cube invariant modulus sheaves with transfers developed by Kahn-Miyazaki-Saito-Yamazaki. From this we deduce refined versions of Ekedahl - and Poincaré duality for crystalline cohomology generalizing results of Mokrane and Nakkajima for reduced D, and a modulus version of Milne-Kato duality for étale motivic cohomology with p-primary torsion coefficients, which refines a result of Jannsen-Saito-Zhao. We furthermore get new integral models for rigid cohomology with compact supports on the complement of D and a modulus version of Milne's perfect Brauer group pairing for smooth projective surfaces over finite fields. |
| title | Duality for Hodge-Witt cohomology with modulus |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2403.18763 |