3 problems

Let $F_p^*$ be the relevant local multiplicative group and let $\widehat{F}_p^*=F_p^*\widehat\otimes\mathbf{Z}_p$. Define $v_p(\mathfrak b)^{\mathrm{an}}\in\widehat{F}_p^*$ from th…

Let $F$ be a totally real field, let $H/F$ be a finite abelian CM extension, and let $\mathfrak p$ split completely in $H$. For a prime ideal $\mathfrak b$ prime to the prescribed…

Let $H/F$ be as in the Brumer–Stark setting, let $L/F$ be a finite abelian CM extension containing $H$, and write $\mathfrak{g}=\operatorname{Gal}(L/F)$ and…