N. Kumakawa

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

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 splits into two distinct primes $\mathfrak{p}$, $\mathfrak{p}'$ in $K$. Assume that $K$ and $p$ satisfies several (somewhat strict) conditi...