Relative Poincaré duality in nonarchimedean geometry
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866909344491110400 |
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| author | Li, Shizhang Reinecke, Emanuel Zavyalov, Bogdan |
| author_facet | Li, Shizhang Reinecke, Emanuel Zavyalov, Bogdan |
| contents | We prove a conjecture of Bhatt-Hansen that derived pushforwards along proper morphisms of rigid-analytic spaces commute with Verdier duality on Zariski-constructible complexes. In particular, this yields duality statements for the intersection cohomology of proper rigid-analytic spaces. In our argument, we construct cycle classes in analytic geometry as well as trace maps for morphisms that are either smooth or proper or finite flat, with appropriate coefficients. As an application of our methods, we obtain new, significantly simplified proofs of $p$-adic Poincaré duality and the preservation of $\mathbf{F}_p$-local systems under smooth proper higher direct images. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_08200 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Relative Poincaré duality in nonarchimedean geometry Li, Shizhang Reinecke, Emanuel Zavyalov, Bogdan Algebraic Geometry Number Theory We prove a conjecture of Bhatt-Hansen that derived pushforwards along proper morphisms of rigid-analytic spaces commute with Verdier duality on Zariski-constructible complexes. In particular, this yields duality statements for the intersection cohomology of proper rigid-analytic spaces. In our argument, we construct cycle classes in analytic geometry as well as trace maps for morphisms that are either smooth or proper or finite flat, with appropriate coefficients. As an application of our methods, we obtain new, significantly simplified proofs of $p$-adic Poincaré duality and the preservation of $\mathbf{F}_p$-local systems under smooth proper higher direct images. |
| title | Relative Poincaré duality in nonarchimedean geometry |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2410.08200 |