10 problems

Wan's conjecture. If

Let $C$ be a generic supersingular hyperelliptic curve of genus $g$ over a field of characteristic $2$. Refined hyperelliptic Oort conjecture. If $g$ is not a power of $2$, then ……

Let $C$ be a generic supersingular hyperelliptic curve of genus $g\geq 2$. Naive hyperelliptic Oort analogue. The automorphism group of $C$ is … The paper immediately explains that…

Automorphism conjecture. The automorphism group of the curve corresponding to the generic point is trivial.

Let $p$ be an odd prime. Let $X'$ be a smooth curve of genus $3$ over $\overline{\mathbf F}_p$, and let $\pi':Y'\to X'$ be a double cover branched at two points. By the Riemann–Hur…

Let $p$ be a prime congruent to $1$ modulo $4$. Consider unramified double covers of smooth curves of genus $3$; such a cover has a smooth curve of genus $5$ as its total space. Su…

Let $L$ be the set of supersingular lambda invariants, let $M'$ be the free module generated by the symbols $[\lambda]$ for $\lambda\in L$, and let $e_0^0$ and $e_0^1$ be the eleme…

Assume $p=3$. Let $L$ be the set of supersingular lambda invariants in $\mathbf{F}_{N^2}$, let $H'$ be the derivative of the associated polynomial $H$, and extend and lift $\log$ t…

Assume $p\geq5$. Let $L$ be the set of supersingular lambda invariants in $\mathbf{F}_{N^2}$, let $H'$ be the derivative of the associated polynomial $H$, and extend $\log$ to a su…

Assume $N$ is a prime with $N\equiv 1\pmod 4$, let $L$ be the set of supersingular lambda invariants in $\mathbf{F}_{N^2}$, and let $H'$ denote the derivative of the polynomial $H$…