3 problems

Grothendieck's section conjecture. If $k$ is of finite type over $\mathbb{Q}$, then: (SC1) the map

Let $X$ and $Y$ be algebraic varieties over a finitely generated field $K$. Write … for the natural map from dominant morphisms from $X$ to $Y$ over $K$ to Galois-compatible open h…

Section-lifting conjecture. If $k$ is a field finitely generated over $\mathbb{Q}$ and $U$ is a nonempty open subset of $X$, then every section of…