Good formal structures for flat meromorphic connections, II: Excellent schemes
Good formal structures for flat meromorphic connections, II: Excellent schemes
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DOI：
10.1090/s0894-0347-2010-00681-9
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发表时间：
2010-01
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影响因子：
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通讯作者：
K. Kedlaya
中科院分区：
文献类型：
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作者：
K. Kedlaya
给出了特征为零的域上优方案上的平坦亚纯联络，证明了爆破后存在良好的形式结构，推广了Mochizuki关于代数簇的一个定理.该论证结合了前一篇论文中良好形式结构的数值标准，以及基于相关赋值空间(Riemann-Zariski空间)几何的分析。我们得到了类似的结果，形式完成了一个优秀的方案沿着封闭子方案。如果我们用一个复杂的解析变量来代替优秀的格式，我们会得到一个类似但更弱的结果，即爆破只能在指定点的一个小邻域内构造。
Given a flat meromorphic connection on an excellent scheme over a field of characteristic zero, we prove existence of good formal structures after blowing up; this extends a theorem of Mochizuki for algebraic varieties. The argument combines a numerical criterion for good formal structures from a previous paper, with an analysis based on the geometry of an associated valuation space (Riemann-Zariski space). We obtain a similar result over the formal completion of an excellent scheme along a closed subscheme. If we replace the excellent scheme by a complex analytic variety, we obtain a similar but weaker result in which the blowup can only be constructed in a small neighborhood of a prescribed point.