4 problems

Let $H\subset\mathbb{A}^n$ be the hypersurface defined by a polynomial $F\in\mathbb{Z}[X_1,\ldots,X_n]$ of degree $d\geq 2$, with absolutely irreducible leading form. Let…

Let $V\subset\mathbb{P}^N$ be an irreducible projective variety, and let $C(V)$ and, where relevant, $\gamma(V)$ be the constants in the Projective Dimension Growth Conjecture. Uni…

Let $V\subset\mathbb{P}^N$ be an irreducible projective variety of degree $d\geq 2$ defined over $\mathbb{Q}$, and let $N_{\mathrm{proj}}(V,B)$ denote the number of rational points…

Let $X\subseteq\mathbb{P}_{\mathbb{Q}}^{M-1}$ be an irreducible projective variety of degree at least two defined over $\mathbb{Q}$. Let $N_X(B)$ be the number of rational points o…