Geodesic
Néron models of Jacobians over bases of arbitrary dimension
Épijournal de Géométrie Algébrique, Tome 6 (2022)

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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.
DOI : 10.46298/epiga.2022.7340
Classification : 14H10, 14H40 
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     author = {Poiret, Thibault},
     title = {N\'eron models of {Jacobians} over bases of arbitrary dimension},
     journal = {\'Epijournal de G\'eom\'etrie Alg\'ebrique},
     publisher = {mathdoc},
     volume = {6},
     year = {2022},
     doi = {10.46298/epiga.2022.7340},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/epiga.2022.7340/}
}
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Poiret, Thibault. Néron models of Jacobians over bases of arbitrary dimension. Épijournal de Géométrie Algébrique, Tome 6 (2022). doi: 10.46298/epiga.2022.7340

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