5 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 $F$…

Assume $p=3$. Let $L$ be the set of supersingular lambda invariants in $\mathbf{F}_{N^2}$, let $H'$ be the derivative of the associated polynomial $H$, and extend and lift $\log$ t…

Assume $p\geq5$. Let $L$ be the set of supersingular lambda invariants in $\mathbf{F}_{N^2}$, let $H'$ be the derivative of the associated polynomial $H$, and extend $\log$ to a su…

Let $M$ be a finite Galois extension of $\mathbb{Q}$), let $G=\operatorname{Gal}(M/\mathbb{Q})$, let $E_p=\operatorname{Emb}(M,\mathbb{C}_p)$, and let…

Let $M$ be a finite Galois extension of $\mathbb{Q}$), let $G=\operatorname{Gal}(M/\mathbb{Q})$, let $E_p=\operatorname{Emb}(M,\mathbb{C}_p)$, and choose $g_j\in G$ and…