6 problems

Let $A$ be an abelian variety over an algebraic number field $k$, and let $k^{\mathrm{ab}}$ be the maximal abelian extension of $k$. The Mordell–Weil group is $A(k^{\mathrm{ab}})$.…

Basis-independent principal-overgroup conjecture.

Rank-greater-than-two conjecture. The original Miasnikov–Ventura–Weil conjecture holds for $H\leq K\leq F_Y$ whenever $|Y|>2$.

Let $\mathcal{ALG}_0$ denote the class of algebraic field extensions of $\mathbb{Q}$ considered in the paper, and let the normal algebraic field extensions of $\mathbb{Q}$ be the s…

Let $H\leq J$ be subgroups of a free group $\mathbf{F}$. Let $\mathbf{F}'$ be a free extension of $\mathbf{F}$, meaning that $\mathbf{F}\leq\mathbf{F}'$ and $\mathbf{F}'$ is free,…

Let $\mathbf{F}$ be a free group, and let $H\leq J\leq\mathbf{F}$. For a basis $X$ of $\mathbf{F}$, write $H\leq_{{\scriptscriptstyle \overset{\twoheadrightarrow}{X}}}J$ when the c…