扩张的缺陷、关键多项式与局部单值化
Defect of an extension, key polynomials and local uniformization
摘要：
对值域的所有单有限扩张，我们证明了它的亏数是相应的关键多项式完备集的有效次数的乘积。作为结果，我们得到了一个局部单值化定理的秩为1的估值为中心的等特征拟优良的局部区域满足一些归纳假设的缺乏缺陷。
英文摘要：
For all simple and finite extension of a valued field, we prove that its defect is the product of the effective degrees of the complete set of key polynomials associated. As a consequence, we obtain a local uniformization theorem for valuations of rank 1 centered on an equicharacteristic quasi-excellent local domain satisfying some inductive assumptions of lack of defect.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
