4 problems

Let $L/H/F$ be a tower in which $F$ is totally real and $H$ and $L$ are finite abelian CM extensions of $F$, with $L$ containing $H$. Write $\mathcal{G}=\operatorname{Gal}(L/F)$,…

Let $u_3\in F_{\mathfrak p}^*\otimes\mathbb Z[G]$ be the element defined by the cap product … Let $u_{\mathfrak p}$ denote the Brumer–Stark element. Third Brumer–Stark formula. … T…

Fix a subset $\Sigma\subseteq\Sigma_S(E)$ satisfying the source's condition, set $r=|\Sigma_S(\mathcal{K}_\infty)|$, $r'=|\Sigma|$, and…

Let $F$, $H$, $S$, $T$, and $\mathfrak{p}$ be as above, and let $L/F$ be a finite abelian CM extension containing $H$ and unramified outside…