Néron models of algebraic curves
Néron models of algebraic curves
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代数曲线的 Néron 模型
DOI：
10.1090/tran/6642
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发表时间：
2013
影响因子：
1.3
通讯作者：
Jilong Tong
中科院分区：
文献类型：
--
作者：
Qing Liu;Jilong Tong
设S是函数域为K的Dedekind概型.本文证明了：如果X_K是K上正亏格的光滑连通真曲线，则它存在S上的Neron模型，即，满足通常Neron映射性质的有限型光滑分离模型。它由S上X_K的极小真正则模型的光滑轨迹给出，与椭圆曲线的情况一样。当S是优秀的，一个类似的结果保持连接光滑仿射曲线不同的仿射线，局部有限型Neron模型。
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 Neron model over S, i.e., a smooth separated model of finite type satisfying the usual Neron 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 Neron models.