2 problems

Let $k$ be a totally real number field, let ${\mathfrak{f}}\neq\mathcal{O}_k$ be a proper integral ideal, let $K=k({\mathfrak{f}})$, let $G=\operatorname{Gal}(K/k)$, and let $S$ be…

Let $k$ be a totally real number field, let ${\mathfrak{f}}\neq\mathcal{O}_k$ be a proper integral ideal, let $K=k({\mathfrak{f}})$ be the associated ray-class field, and write…