8 problems

Let $X$ be a smooth curve over a finite field of characteristic $p$, let $E$ be a number field, and let ${\mathbf{L}}=\{{\mathcal{L}}_\lambda\}$ be an $E$-compatible system of liss…

Alternating-group monodromy conjecture. All of the $[1,1]$-origamis in Theorem have monodromy group isomorphic to $\operatorname{Alt}_{2g-1}$.

Let $f:X\rightarrow \mathbb P^1$ be an indecomposable covering of degree $n$, with $X$ of genus $g_X=g$, and let $\operatorname{Mon}(f)$ denote its monodromy group. For each intege…

Let $f\colon V\hookrightarrow U$ be an open sub-curve, let $u\in V({\mathbb{F}}_{q^e})$ be a base point, and let ${\mathcal{F}}$ be a convergent $F$-isocrystal on $U$. Write…

Let ${\mathcal{F}}$ be a convergent $F$-isocrystal on the curve $U$, fix $u\in U({\mathbb{F}}_{q^e})$, and let $\operatorname{Gr}({\mathcal{F}}/U,u)$ be its monodromy group over…

Let $U$ be the curve, let $K$ be the specified finite totally ramified extension, and let ${\mathcal{F}}$ be a convergent $F$-isocrystal on $U$. Fix $u\in U({\mathbb{F}}_{q^e})$, a…

Consider the 14 rank-$4$ hypergeometric local systems that could arise as the middle cohomology of families of Calabi–Yau threefolds with $h^{2,1}=1$. For these systems, let … be t…

Let $H(\alpha,\beta)$ denote a hyperbolic hypergeometric monodromy group, where $\alpha$ and $\beta$ are the parameter tuples defining the corresponding hypergeometric equation. A…