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arXiv · 1312.4822

N\'eron models of algebraic curves

Qing Liu·Jilong Tong
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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 N\'eron model over S, i.e., a smooth separated model of finite type satisfying the usual N\'eron 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 N\'eron models.

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Qing Liu, Jilong Tong. 2013-12-17. N\'eron models of algebraic curves. https://doi.org/10.1090/tran/6642

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