2 problems

Let $R=\{\mathfrak p_1,\ldots,\mathfrak p_r\}$, let $E_R^*$ be the group of totally positive $R$-units, let $\vartheta\in H_{n+r-1}(E_R^*,\mathbf Z)\cong\mathbf Z$ be a generator,…

Let $F$ be a number field, let $H/F$ be a finite cyclic CM extension, let $p$ be a prime, and let $R$, $R_0$, and $R_1$ be the subsets of primes of $F$ above $p$ that split, ramify…