论文标题
Neukirch-uchida定理具有限制性分支
The Neukirch-Uchida theorem with restricted ramification
论文作者
论文摘要
让$ k $为一个数字字段，$ s $一组$ k $。我们为$ k $ $ k $在$ s $之外和$ g_ {k，s} $的最大扩展中编写$ k_s/k $。在本文中，我们在某些假设下证明了Neukirch-uchida定理的以下概括：“对于$ i = 1,2 $，让$ k_i $是一个数字字段，而$ s_i $ $ k_i $。$ k_i $。是同构。”在这里，主要的假设是至少一个$ i $的$ s_i $的dirichlet密度不是零。证明的关键步骤是从理论上恢复组的$ l $ -ADIC CYCLOTOMIC特征的开放子组为$ g_ {k，s} $的某些质量数量$ l $。
Let $K$ be a number field and $S$ a set of primes of $K$. We write $K_S/K$ for the maximal extension of $K$ unramified outside $S$ and $G_{K,S}$ for its Galois group. In this paper, we prove the following generalization of the Neukirch-Uchida theorem under some assumptions: "For $i=1,2$, let $K_i$ be a number field and $S_i$ a set of primes of $K_i$. If $G_{K_1,S_1}$ and $G_{K_2,S_2}$ are isomorphic, then $K_1$ and $K_2$ are isomorphic." Here the main assumption is that the Dirichlet density of $S_i$ is not zero for at least one $i$. A key step of the proof is to recover group-theoretically the $l$-adic cyclotomic character of an open subgroup of $G_{K,S}$ for some prime number $l$.
