4 problems

Let $f:X_0\to\mathscr{S}_{\mathbf{I},F_{\infty}}^{\operatorname{ord}}$ be a locally closed immersion, and let $X$ be its image. Suppose that $X$ possesses a Zariski-dense collectio…

Let $(X,x)$, $X_0$, and $f$ be as in the source, let $u\in\operatorname{fpl}(\Q)$, and let $G(\L_{\mathbf{I},u,X_0},x)$ and $\operatorname{Lg}(f)_{\Q_u}$ be the groups defined ther…

Let $f:X_0\to\mathscr{S}_{\mathbf{I},F_{\infty}}^{\operatorname{ord}}$ be a locally closed immersion, so that $X$ is a subvariety of…

Let $(X,x)$, $X_0$, $f$, and $\T_{f,x}$ be as in the source, with $f:X_0\to X$ and with $\T_{f,x}$ the associated Tate-linear formal object. Let…