Abelian $p$-extensions with restricted $p$-ramification and the cyclotomic ${\mathbb{Z}}_2$-extension of $\mathbb{Q}(\sqrt{q})$

Tsuyoshi Itoh, Naoki Kumakawa

We develop Hachimori's study on the unramified Iwasawa modules using extensions with restricted $p$-ramification. Let $K$ be an algebraic number field, and $p$ a prime number which…