8 problems

Steingart's surjectivity conjecture. The map $\operatorname{comp}$ is surjective after taking $H^1$, namely

Let $\pi$ be as in the preceding construction, let $D_A(\pi)$ be the associated étale $(\varphi,\mathcal{O}_K^{\times})$-module over $A$, and let $D_A^{\otimes}$ be the functor fro…

Let $A$ be a compact abelian Lie group, let $B$ be a subgroup of $A$, let $E$ be a Landweber exact spectrum, and let $\Phi^B$ denote geometric fixed points. For an $A$-space or $A$…

Let $V$ be a representation for which the $L$-analytic $p$-adic $L$-function $L_p(V)$ is defined, and let $\widetilde{H}^2(V)$ be the Selmer group described above over the $L$-anal…

Let $R_n$ be the Lubin–Tate ring associated to the Honda formal group law $\mathbb{H}_n$ of height $n$ over $\mathbb{F}_{p^n}$, with $R_n\cong \mathbb{W}[[u_1,\ldots,u_{n-1}]]$, wh…

Let $K$ be a finite extension of $\mathbf{Q}_p$, let $K_\infty/K$ be a Lubin–Tate extension, and let $(\varphi,\Gamma)$-modules be the modules attached to $p$-adic representations…

Let $K$ be the finite extension of the maximal unramified extension of a finite extension of $\mathbb{Q}_p$ considered in the paper, let $F$ be its coefficient field, and let $V$ b…

Optimality conjecture. This bound is optimal for all choices of $K$ and $P$.