5 problems

Let $K$ be a number field and let $Z/K$ be a smooth projective irreducible variety of dimension $d$. Define the Albanese kernel by … Here $\mathrm{CH}^d(Z)_0$ is the group of homol…

Let $(X,D)$ be a C-pair, meaning a pair consisting of a complex space $X$ and a boundary divisor $D$ with Campana's orbifold multiplicities, and suppose that $X$ is compact Kähler.…

Let $X$ be a smooth projective variety with $\kappa(X)=0$, and let $\alpha:X\rightarrow A$ be its Albanese map, with general fibre $F$. Ueno Conjecture K. The map $\alpha$ is surje…

Beauville's conjecture. If

Let $K$ be a global field with separable closure $K^s$, and let $X^s$ be a smooth projective variety over $K^s$. Let $\operatorname{CH}_0(X^s)^0$ denote the degree-zero Chow group…