Log smooth extension of a family of curves and semi-stable reduction
Log smooth extension of a family of curves and semi-stable reduction
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DOI：
10.1090/s1056-3911-03-00338-2
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发表时间：
2004-05
影响因子：
1.8
通讯作者：
Takeshi Saito
中科院分区：
文献类型：
--
作者：
Takeshi Saito
总结：我们证明了一个家庭的光滑稳定的曲线上定义的内部的一个日志定期计划扩展到一个日志光滑计划在整个日志定期计划，如果它是这样的边界的每个一般点，在一个非常温和的假设。我们还包括一个事实证明，一个离散估值环上的对数平滑计划有可能是一个半稳定的模型。因此，我们证明了在[10]意义下的离散赋值域上的双曲多曲线，如果剩余域的特征足够大，则可能具有适当的半稳定模型。
Summery: We show that a family of smooth stable curves defined on the interior of a log regular scheme is extended to a log smooth scheme over the whole log regular scheme, if it is so at each generic point of the boundary, under a very mild assumption. We also include a proof of the fact that a log smooth scheme over a discrete valuation ring has potentially a semi-stable model. As a consequence, we show that a hyperbolic polycurve in the sense of [10] over a discrete valuation field has potentially a proper semi-stable model if the characteristic of the residue field is sufficiently large.