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- W2897064003 abstract "Let $k_infty$ be the cyclotomic $mathbb{Z}_p$-extension of an algebraic number field $k$. We denote by $S$ a finite set of prime numbers which does not contain $p$, and $S(k_infty)$ the set of primes of $k_infty$ lying above $S$. In the present paper, we will study the structure of the Galois group $mathcal{X}_S (k_infty)$ of the maximal pro-$p$ extension unramified outside $S (k_infty)$ over $k_infty$. We mainly consider the question whether $mathcal{X}_S (k_infty)$ is a non-abelian free pro-$p$ group or not. In the former part, we treat the case when $k$ is an imaginary quadratic field and $S = emptyset$ (here $p$ is an odd prime number which does not split in $k$). In the latter part, we treat the case when $k$ is a totally real field and $S neq emptyset$." @default.
- W2897064003 created "2018-10-26" @default.
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- W2897064003 date "2018-10-24" @default.
- W2897064003 modified "2023-09-27" @default.
- W2897064003 title "On the structure of the Galois group of the maximal pro-$p$ extension with restricted ramification over the cyclotomic $mathbb{Z}_p$-extension" @default.
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