3 problems

Let $F$ be a totally real field in which $p$ is inert. Let $\tauin X_p$ be a point attached to an oriented integral ideal as above, let $H$ be the narrow Hilbert class field of $F$…

Let $g$ be a weight one modular form, let $g^*$ be its dual, and let $u_1$ denote the unit attached to the associated Galois representation. Let $\kappa(g_{\alpha},g_{1/\alpha}^*)$…

Assume, in addition to the Stark setup, that $F$ is totally real, $K$ is a CM-field, $v$ is a finite place above a rational prime $p$, and $S$ contains all places of $F$ above $p$.…