3 problems

Let $F=\mathbb{Q}$ and let $X$ be a hyperbolic curve. For the étale unipotent fundamental group $U^{\mathrm{et}}$ and its level-$n$ quotient $U_n^{\mathrm{et}}$, let…

Localisation injectivity and vanishing conjecture. For all $0\leq i\leq n$, this map is injective, and

The curves under consideration are higher-genus hyperelliptic curves with explicitly constructed rational points. Kim's Selmer-variety conjecture. There is some higher-dimensional…