2 problems

Assume $p\equiv 1\pmod 4$. Let $C$ be a hyperelliptic curve of genus at least $3$ whose branch points are all defined over $\mathbb{F}_p$. Rational-branch-point p-rank conjecture.…

Let $G$ be an arbitrary finite group, and let $p$ be a prime dividing $|G|$. For a finite group $H$, define its $p$-rank $\operatorname{rk}_p(H)$ to be the maximum rank of an eleme…