4 problems

Let $k$ be a field of characteristic $p>0$, and let a cyclic extension mean a finite Galois extension with cyclic Galois group. Oort's conjecture. Every cyclic extension lifts to c…

Hajir–Maire's conjecture. There exist a totally imaginary number field $K_0$ and a cyclic extension $K/K_0$ of degree $m$ such that $K$ is $p$-rational; moreover, the statement is…

DFK conjecture. The following predictions hold: if $p=3$, then, as $X\to\infty$,

Non-genus $\varepsilon$-conjecture. Except for subfamilies of density zero,