8 problems

Let $A$ be a generic supersingular principally polarized abelian variety of dimension $g\geq 2$, and let $\mathbb Z_m$ denote the cyclic group of order $m$. Oort's conjecture. The…

Artin's conjecture. Every Artin-supersingular K3 surface $X$ is supersingular.

Let $S$ be a K3 surface in characteristic $2$, let $h\in\mathbb{N}\setminus\{0\}\cup\{\infty\}$ be the height of its formal Brauer group, and let $\rho(S)$ denote its Picard number…

Oort's conjecture. There is a dense open subscheme of $\mathscr S_g$ on which

Supersingularity conjecture. If $X$ is second-Artin supersingular, then:

Oort's conjecture. The automorphism group of $(X,\lambda)$ is

Tate conjecture. The surface $X$ is Artin supersingular if and only if it is Shioda supersingular.

Mixed-type conjecture. A supersingular abelian surface over $F_q$ most likely has mixed type.