4 problems

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…

Let $u_2=\sum_{\sigma\in G}u_2(\sigma)\otimes[\sigma^{-1}]\in F_{\mathfrak p}^*\otimes\mathbb Z[G]$ be the element obtained from the Eisenstein cocycle and the cap-product construc…

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…