Néron models of algebraic curves
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- by Qing Liu and Jilong Tong PDF
- Trans. Amer. Math. Soc. 368 (2016), 7019-7043 Request permission
Abstract:
Let $S$ be a Dedekind scheme with field of functions $K$. We show that if $X_K$ is a smooth connected proper curve of positive genus over $K$, then it admits a Néron model over $S$, i.e., a smooth separated model of finite type satisfying the usual Néron mapping property. It is given by the smooth locus of the minimal proper regular model of $X_K$ over $S$, as in the case of elliptic curves. When $S$ is excellent, a similar result holds for connected smooth affine curves different from the affine line, with locally finite type Néron models.References
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Additional Information
- Qing Liu
- Affiliation: Institut de Mathématiques de Bordeaux, CNRS UMR 5251, Université de Bordeaux, 33405 Talence, France
- MR Author ID: 240790
- Email: Qing.Liu@math.u-bordeaux1.fr
- Jilong Tong
- Affiliation: Institut de Mathématiques de Bordeaux, CNRS UMR 5251, Université de Bordeaux, 33405 Talence, France
- Email: Jilong.Tong@math.u-bordeaux1.fr
- Received by editor(s): December 17, 2013
- Received by editor(s) in revised form: September 2, 2014
- Published electronically: December 21, 2015
- © Copyright 2015 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 368 (2016), 7019-7043
- MSC (2010): Primary 14H25, 14G20, 14G40, 11G35
- DOI: https://doi.org/10.1090/tran/6642
- MathSciNet review: 3471084
Dedicated: Dedicated to Michel Raynaud on the occasion of his seventy-fifth birthday