4 problems

Let $(K,v)$ be a valued field, and let an Artin–Schreier (AS) tower mean a tower $M/K$ formed through Artin–Schreier extensions. Assume that $(K,v)$ is Henselian, perfect, and has…

Primitive-root conjecture. The element $\theta$ is primitive in $\mathbb{F}_{p^p}$; equivalently, its multiplicative order is $p^p-1$.

Assume that $q$ is a prime power with $q\equiv2\pmod3$, let $K=\mathbb{F}_{q^2}(u)$ with $u^q-u=t$, and let $E$ be the elliptic curve $Y^2+tY=X^3$. Let $V$ be the subgroup of…

Let $q ottextarea?$. In the setting where $qequiv 2pmod 3$, let $E$ be the elliptic curve $Y^2+tY=X^3$ over $K=mathbb{F}{q^2}(u)$ with $u^q-u=t$, and let $V$ be the subgroup of…