GALOIS GROUPS WITH PRESCRIBED RAMIFICATION
GALOIS GROUPS WITH PRESCRIBED RAMIFICATION
复制标题
具有指定分枝的伽罗瓦群
DOI：
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
D. Harbater
中科院分区：
文献类型：
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作者：
D. Harbater
本文研究了函数域和数域情况下具有给定分支位置集的伽罗瓦群。在几何情况下，特征 p 表明删除了 r > 0 点的亏格 g 曲线的基本群取决于曲线和点的选择，而不仅仅是 g 和 r（与特征 0 不同）。在算术情况下，某些群被证明在具有给定分枝的 Q 上出现，或者被证明不出现，特别是当唯一的分枝素数为 2 时。
The paper studies Galois groups with a given set of ramified places, in both the function field and number field cases. In the geometric case, it is shown in characteristic p that the fundamental group of a curve of genus g with r > 0 points deleted depends upon the choice of curve and points, and not just on g and r (unlike in characteristic 0). In the arithmetic case, certain groups are shown to occur over Q with given ramification, or are shown not to occur, particularly when the only ramified prime is 2.