3 problems

Corvaja–Zannier's conjecture. Any smooth projective variety with a potentially dense set of rational points has the weak Hilbert property potentially.

The puncturing conjectures. The following statements hold:

Let $R$ be an arithmetic ring with fraction field $k$, and let $\mathcal{X}$ be a regular quasi-projective arithmetic scheme over $R$. Write $\mathcal{X}(R)^{(1)}$ for the relevant…