On the Brauer groups of fibrations
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866909348297441280 |
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| author | Qin, Yanshuai |
| author_facet | Qin, Yanshuai |
| contents | Let $\mathcal{X}\rightarrow C$ be a dominant morphism between smooth irreducible varieties over a finitely generated field $k$ such that the generic fiber $X$ is smooth, projective and geometrically connected. Assuming that $C$ is a curve with function field $K$, we build a relation between the Tate-Shafarevich group for $\mathrm{Pic}^0_{X/K}$ and the geometric Brauer groups for $\mathcal{X}$ and $X$, generalizing a theorem of Artin and Grothendieck for fibered surfaces to arbitrary relative dimension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2012_01324 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | On the Brauer groups of fibrations Qin, Yanshuai Algebraic Geometry Number Theory 14F22 Let $\mathcal{X}\rightarrow C$ be a dominant morphism between smooth irreducible varieties over a finitely generated field $k$ such that the generic fiber $X$ is smooth, projective and geometrically connected. Assuming that $C$ is a curve with function field $K$, we build a relation between the Tate-Shafarevich group for $\mathrm{Pic}^0_{X/K}$ and the geometric Brauer groups for $\mathcal{X}$ and $X$, generalizing a theorem of Artin and Grothendieck for fibered surfaces to arbitrary relative dimension. |
| title | On the Brauer groups of fibrations |
| topic | Algebraic Geometry Number Theory 14F22 |
| url | https://arxiv.org/abs/2012.01324 |