论文标题
在驯服上
On tame ${\mathbb Z}/p{\mathbb Z}$ extensions with prescribed ramification
论文作者
论文摘要
The tame Gras-Munnier Theorem gives a criterion for the existence of a ${\mathbb Z}/{\mathbb Z}$-extension of a number field $K$ ramified at exactly a set $S$ of places of $K$ prime to $p$ (allowing real Archimedean places when $p=2$) in terms of the existence of a dependence relation on the Frobenius elements of these places in a certain管理扩展。我们给出了该定理的新的，更简单的证据，该定理也将$ K $的此类扩展名与这些依赖关系集有关。在提出了此证明之后，我们使用基于全球二元性的更复杂的威尔·格林贝格公式来谴责关键命题3。
The tame Gras-Munnier Theorem gives a criterion for the existence of a ${\mathbb Z}/{\mathbb Z}$-extension of a number field $K$ ramified at exactly a set $S$ of places of $K$ prime to $p$ (allowing real Archimedean places when $p=2$) in terms of the existence of a dependence relation on the Frobenius elements of these places in a certain governing extension. We give a new and simpler proof of this theorem that also relates the set of such extensions of $K$ to the set of these dependence relations. After presenting this proof, we then reprove the key Proposition 3 using the more sophisticated Wiles-Greenberg formula based on global duality.
