7 problems

Conjecture Fconst. The subset

Conjecture F+. The subset

Conjecture F. The subset

Let $k$ be a number field, let $P_1(t),\cdots, P_n(t)$ be pairwise distinct irreducible polynomials in $k[t]$. Set $k_i=k[t]/(P_i(t))$, let $a_i$ be the class of $t$ in $k_i$, let…

Harari–Wittenberg's conjecture. The set

Weak locally split values conjecture. There exists $t_0\in k$ satisfying condition (2) of the strong conjecture, while condition (1) is replaced by: $t_0$ is arbitrarily close to…

Strong locally split values conjecture. There exists $t_0\in k$ such that $t_0$ is arbitrarily close to $t_v$ for every $v\in S$, and, for every $i$ and every finite place $w$ of…