Weil's Theorem (1940–1948)
Given a smooth algebraic curve of genus g defined over the field with p elements,
its number of points over the field with pⁿ elements is $$ p^n - \alpha_1^n - \cdots - \alpha_{2g}^n + 1 $$ where all the \(\alpha_i \in \mathbb{C}\) have \(|\alpha_i| = \sqrt{p}\).