The Principle of Quadratic Chabauty and Nonsplit Cartan Modular Curves

The Principle of Quadratic Chabauty and Nonsplit Cartan Modular Curves

Explore the advanced mathematical concept of quadratic Chabauty and its application to nonsplit Cartan modular curves in this lecture by Samuel Le Fourn. Delve into the intricate world of arithmetic geometry, focusing on the study of rational points on modular curves. Gain insights into the theoretical and computational aspects of determining K-rational points on modular curves XH(K) for various fields and subgroups. Examine the geometry of modular curves, their Q-rational points, and both classical and non-abelian Chabauty methods. Discover how this principle contributes to the broader field of rational points on varieties, a topic of special interest to arithmetic geometers.