Manin–Drinfeld theorem

The Manin–Drinfeld theorem is a significant result in the field of algebraic geometry and number theory, particularly in the study of rational points on algebraic curves. It was developed independently by mathematicians Yuri Manin and Vladimir Drinfeld in the 1970s. The theorem deals with the existence and structure of rational points on certain types of algebraic varieties, especially in the context of curves defined over non-closed fields, such as the rational numbers \(\mathbb{Q}\).