3 problems

Divisible-plus-finite conjecture. The group $F^2(X)$ is the direct sum of a divisible group and a finite group.

Let $X$ be a smooth projective geometrically connected variety over a number field $K$ with a $K$-rational point. For a finite place $v$ of $K$, let … be the base change to the com…

Let $U$ be a smooth algebraic surface, let $p_g(U)$ denote its geometric genus, and let $T(U)$ be the Albanese kernel, namely the kernel of the Albanese morphism…