Mod-p Poincaré Duality in p-adic Analytic Geometry
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866914687050842112 |
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| author | Zavyalov, Bogdan |
| author_facet | Zavyalov, Bogdan |
| contents | We show Poincaré Duality for $\mathbf{F}_p$-étale cohomology of a smooth proper rigid-analytic space over a non-archimedean field $K$ of mixed characteristic $(0, p)$. It positively answers the question raised by P. Scholze in [Sch13a]. We prove duality via constructing Faltings' trace map relating Poincaré Duality on the generic fiber to (almost) Grothendieck Duality on the mod-$p$ fiber of a formal model. We also formally deduce Poincaré Duality for $\mathbf{Z}/p^n\mathbf{Z}$, $\mathbf{Z}_p$, and $\mathbf{Q}_p$-coefficients. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_01830 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Mod-p Poincaré Duality in p-adic Analytic Geometry Zavyalov, Bogdan Algebraic Geometry Number Theory We show Poincaré Duality for $\mathbf{F}_p$-étale cohomology of a smooth proper rigid-analytic space over a non-archimedean field $K$ of mixed characteristic $(0, p)$. It positively answers the question raised by P. Scholze in [Sch13a]. We prove duality via constructing Faltings' trace map relating Poincaré Duality on the generic fiber to (almost) Grothendieck Duality on the mod-$p$ fiber of a formal model. We also formally deduce Poincaré Duality for $\mathbf{Z}/p^n\mathbf{Z}$, $\mathbf{Z}_p$, and $\mathbf{Q}_p$-coefficients. |
| title | Mod-p Poincaré Duality in p-adic Analytic Geometry |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2111.01830 |