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摘要翻译：
我们研究了在一个温和的分支基扩张是充分的情况下曲线的稳定约简。如果X是定义在严格henselian离散赋值环的分式域上的光滑曲线，则根据T.Saito的一个判据，它根据具有严格法交的极小模型的几何，精确地描述了当一个温和的分枝扩张足以使X获得稳定的约简时。对于这类曲线，我们构造了一个实现稳定约简的显式扩张，并进一步证明了这种扩张是极小的。我们还得到了Saito判据的纯几何证明，避免了消失循环的使用。
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英文标题：
《Stable reduction of curves and tame ramification》
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作者：
Lars Halvard Halle
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最新提交年份：
2007
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分类信息：
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
We study stable reduction of curves in the case where a tamely ramified base extension is sufficient. If X is a smooth curve defined over the fraction field of a strictly henselian discrete valuation ring, there is a criterion, due to T. Saito, that describes precisely, in terms of the geometry of the minimal model with strict normal crossings of X, when a tamely ramified extension suffices in order for X to obtain stable reduction. For such curves we construct an explicit extension that realizes the stable reduction, and we furthermore show that this extension is minimal. We also obtain purely geometric proof of Saito's criterion, avoiding the use of vanishing cycles.
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PDF链接：
https://arxiv.org/pdf/0711.0896
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