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Néron models of algebraic curves


Authors: Qing Liu and Jilong Tong
Journal: Trans. Amer. Math. Soc. 368 (2016), 7019-7043
MSC (2010): Primary 14H25, 14G20, 14G40, 11G35
DOI: https://doi.org/10.1090/tran/6642
Published electronically: December 21, 2015
MathSciNet review: 3471084
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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.


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Additional Information

Qing Liu
Affiliation: Institut de Mathématiques de Bordeaux, CNRS UMR 5251, Université de Bordeaux, 33405 Talence, France
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

DOI: https://doi.org/10.1090/tran/6642
Keywords: N\'eron model, curve, good reduction
Received by editor(s): December 17, 2013
Received by editor(s) in revised form: September 2, 2014
Published electronically: December 21, 2015
Dedicated: Dedicated to Michel Raynaud on the occasion of his seventy-fifth birthday
Article copyright: © Copyright 2015 American Mathematical Society

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