8 problems

Let $A^h$ be a local chart arising from the Bambozzi–Kremnizer spectrum of a Banach algebra over $\mathbb{Q}_p$ or $\mathbb{F}_p((t))$, and let $S$ be the coefficient ring. For int…

Let $\mathcal R_{\mathbb Q}=\bigcup_N\mathcal R_{1/N}$ be the rational Robba ring over $\mathbb C_p$, completed under the Gauss norm. Rational Robba-ring admissibility conjecture.…

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

Let $X$ be as in the paper, let $n\geq 2$, let $G(X)$ be a reductive group, and let $\Pi_X[\log(1+T)^{1/n}]$ be the generalized Robba ring in the imperfect setting. Let…

Invariant field conjecture. In general,

Convergence conjecture. If $h\in\mathcal{R}$ is such that $\varphi(h)$ is convergent on the annulus

Invariants conjecture. If $\varphi$ is overconvergent, then

Let $G$ act continuously on $\tilde{\mathbf{A}}^{\dagger,r}_{L_\infty}$, and let $\tilde{\mathbf{A}}^{\dagger,r,\operatorname{aff}}_{K_\infty}$ be the subring of elements admitting…