3 problems

Let $X_0$ be a geometric connected smooth variety over $\mathbb{F}_q$, let $f_0:X_0\rightarrow \mathscr{A}_{g,\mathbb{F}_q}^{{\mathrm{ord}}}$ be a morphism as above, and let $A$ be…

Let $X$ be a smooth rigid-analytic space over a $p$-adic field $K$, and let $\mathbb{L}$ be a de Rham $\mathbb{Q}_p$-local system on $X$. A point $x\in X$ has rank $1$ if it is a r…

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…