3 problems

Let $U \subset \mathbb{A}^3$ be a cubic surface that is smooth and log K3 over $\mathbb{Q}$ and defined by a cubic polynomial $f \in \mathbb{Z}[x_1,x_2,x_3]$. Let $N_U^\circ(B)$ co…

The logarithmic-bound conjecture. As $B\to\infty$,

Integral-point counting conjecture. There exists a Zariski open subset $\mathcal{U} \subseteq \mathcal{X}$ and a constant $b$ such that