4 problems

Let $H_g$ be the number field cut out by the Artin representation attached to the adjoint of $g$, and let $H_{g,p}$ be a completion of $H_g$ at a prime above $p$. Let…

Let $F$ be a real quadratic field, let $H/F$ be the relevant narrow Hilbert class field, let $G=\operatorname{Gal}(H/F)$, let $\mathfrak P$ be a prime above $p$, and let…

Let $g$ be a modular form, let $p$ be a prime, let $\mathcal{L}_{g_\alpha}$ be the associated $p$-adic $L$-invariant, and let $u_{g_\alpha}$ be the Gross–Stark unit attached to…

Tate–Gross conjecture. For every $\sigma\in G$, $u_{S,T,\sigma}\in{\mathscr E}_{\mathfrak p}$; for every $\sigma\in G$ and every ${\mathfrak q}\in T$,…