论文标题
牛顿 - 纯曲舍克斯算法的概括用于半模型
A generalization of the Newton-Puiseux algorithm for semistable models
论文作者
论文摘要
在本文中，我们给出了一种算法，该算法可以在完全离散值的字段上计算曲线的温和覆盖的骨骼。该算法依赖于{驯服同时可半固定的还原定理}，为此我们提供了一个简短的证明。为了在实践中使用该定理，我们表明我们可以使用兼容的功率系列找到正常化的主要理想链的扩展。这使我们可以重建盖子的骨架。在研究功率序列与主要理想的扩展之间的联系时，我们从数字理论（例如Kummer-Dedekind定理）和Dedekind定理中获得了经典定理的概括，用于Galois组的循环定理。
In this paper we give an algorithm that calculates the skeleton of a tame covering of curves over a complete discretely valued field. The algorithm relies on the {tame simultaneous semistable reduction theorem}, for which we give a short proof. To use this theorem in practice, we show that we can find extensions of chains of prime ideals in normalizations using compatible power series. This allows us to reconstruct the skeleton of the covering. In studying the connections between power series and extensions of prime ideals, we obtain generalizations of classical theorems from number theory such as the Kummer-Dedekind theorem and Dedekind's theorem for cycles in Galois groups.
