Elimination of ramification I: The generalized stability theorem
Elimination of ramification I: The generalized stability theorem
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消除分枝I：广义稳定性定理
DOI：
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发表时间：
2010
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通讯作者：
F. Kuhlmann
中科院分区：
文献类型：
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作者：
F. Kuhlmann
我们证明了“稳定性定理”的一个一般形式：如果K是一个值域，使得它的分支理论亏损对它的所有有限扩张都是平凡的，并且如果F| K是值域的一个非生成的（超越）扩张，对于它，Abhyankar不等式中的等式成立，那么对于F的所有有限扩张，亏损也是平凡的。这个定理被应用于消除这类值函数域上的分歧。它在局部一致化和正特征值域的模型论中有应用。
We prove a general version of the "Stability Theorem": if K is a valued field such that the ramification theoretical defect is trivial for all of its finite extensions, and if F|K is a finitely generated (transcendental) extension of valued fields for which equality holds in the Abhyankar inequality, then the defect is also trivial for all finite extensions of F. This theorem is applied to eliminate ramification in such valued function fields. It has applications to local uniformization and to the model theory of valued fields in positive characteristic.