Néron models of Jacobians over bases of arbitrary dimension
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arXiv
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866912632719540224 |
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| author | Poiret, Thibault |
| author_facet | Poiret, Thibault |
| contents | We work with a smooth relative curve $X_U/U$ with nodal reduction over an excellent and locally factorial scheme $S$. We show that blowing up a nodal model of $X_U$ in the ideal sheaf of a section yields a new nodal model, and describe how these models relate to each other. We construct a Néron model for the Jacobian of $X_U$, and describe it locally on $S$ as a quotient of the Picard space of a well-chosen nodal model. We provide a combinatorial criterion for the Néron model to be separated. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2103_06917 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Néron models of Jacobians over bases of arbitrary dimension Poiret, Thibault Algebraic Geometry Commutative Algebra Number Theory We work with a smooth relative curve $X_U/U$ with nodal reduction over an excellent and locally factorial scheme $S$. We show that blowing up a nodal model of $X_U$ in the ideal sheaf of a section yields a new nodal model, and describe how these models relate to each other. We construct a Néron model for the Jacobian of $X_U$, and describe it locally on $S$ as a quotient of the Picard space of a well-chosen nodal model. We provide a combinatorial criterion for the Néron model to be separated. |
| title | Néron models of Jacobians over bases of arbitrary dimension |
| topic | Algebraic Geometry Commutative Algebra Number Theory |
| url | https://arxiv.org/abs/2103.06917 |