Stable reduction of curves and tame ramification
Stable reduction of curves and tame ramification
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曲线稳定减少并控制后果
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发表时间：
2007
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通讯作者：
L. H. Halle
中科院分区：
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作者：
L. H. Halle
研究了曲线的稳定约化问题，给出了曲线的光滑分歧基扩张的充分条件。如果X是定义在一个严格亨塞尔离散赋值环的分数域上的光滑曲线，则有一个标准，由于Saito，它精确地描述了，在X的严格法向交叉的最小模型的几何方面，当一个tamely分歧扩展足以使X获得稳定的约化时。对于这样的曲线，我们构造了一个明确的扩展，实现稳定的减少，我们还表明，这种扩展是最小的。我们还得到了Saito判据的一个新的证明，避免了使用上同调和消失圈。
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 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 a new proof of Saito’s criterion, avoiding the use of ℓ-adic cohomology and vanishing cycles.