10 problems

Let $V$ be an $o_L$-linear representation of $G_L$, let $M_{\mathrm{LT}}=\mathbb{D}(V)$ be an étale $L$-analytic $(\varphi_L,\Gamma_L)$-module over $\mathbf{A}_L$, and let…

Let $L$ be a finite extension of $\mathbb{Q}_p$, let $K$ be a coefficient field containing $L$, and let $M_0$ be an $L$-analytic $(\varphi_L,\Gamma_L)$-module over $\mathcal{R}_L$.…

Let $L$ be a finite extension of $\mathbb{Q}_p$, let $K$ be a coefficient field containing $L$, and let $V$ be an $L$-analytic $o_L$-linear representation of $G_L$. Let $M$ be the…

Pessimistic conjecture. The image of this map is closed in the Banach-space topology of $H^1(\mathcal{K}_\infty,V)$. This weaker assertion is stated as sufficient for the paper's p…

Let $F$ be the coefficient field, let $\mathcal{R}_F$ be its Robba ring, and let $\mathcal{D}$ be a $(\varphi,\Gamma)$-module over $\mathcal{R}_F$. For a representation $V$ of…

Nakayama's local epsilon conjecture. There exists an isomorphism

Equivalence conjecture. The functors $D_X$ and $D_X^{\operatorname{perf}}$ each define an equivalence of categories. This conjecture predicts that the comparison between the overco…

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…

Local freeness conjecture. For every $(\varphi,\Gamma_K)$-module $M$ over $\mathcal{R}_A(\pi_K)$, there exists a finite admissible cover $\{\operatorname{Max}(A_i)\}_{i=1,\dots,n}$…

Extension conjecture. The claim of the theorem and the corollary also holds true if one replaces $x_0$ by a (locally) closed subscheme of the special fiber over which there exists…