Arithmetic Field Theory for Elliptic Curves by Minhyong Kim

Explore the intricacies of arithmetic field theory for elliptic curves in this comprehensive lecture by Minhyong Kim. Delve into the fascinating world of rational points on modular curves, a key area of interest for arithmetic geometers. Gain advanced insights into the geometry of modular curves, their Q-rational points, and both classical and non-abelian Chabauty methods. Learn about the theoretical and computational aspects of determining K-rational points on modular curves XH(K) for various fields and subgroups. Discover the connections between elliptic curves, modular forms, and modular curves as central objects in arithmetic geometry. Benefit from a balanced approach that covers both advanced topics and practical examples, making this lecture suitable for researchers at various levels of expertise.