2 problems

Assume $K=K_{{\mathrm{cyc}}}\cap K_\infty$. Let $\mathfrak M$ be a crystalline Breuil–Kisin module of rank $d$, let $\lambda:=\frac{\xi}{E([\pi^{\flat}])}$, and let $\widetilde A$…

Let $\Gamma$ be the congruence subgroup under consideration and let $\eta$ be the associated coefficient character. A Galois representation attached to a Hecke eigenclass in…