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arXiv · 2103.06917

N\'eron models of Jacobians over bases of arbitrary dimension

Thibault Poiret
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Abstract

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 N\'eron 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 N\'eron model to be separated.

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Thibault Poiret. 2021-03-11. N\'eron models of Jacobians over bases of arbitrary dimension. https://doi.org/10.46298/epiga.2022.7340

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