Conjectural Asymptotics of Prime Orders of Points on Elliptic Curves Over Number

Explore the conjectural asymptotics of prime orders of points on elliptic curves over number fields in this comprehensive lecture by Michael Stoll. Delivered as part of the "Rational Points on Modular Curves" program at the International Centre for Theoretical Sciences, this 1-hour 13-minute talk delves into advanced topics in arithmetic geometry. Gain insights into the theoretical aspects of elliptic curves, modular forms, and modular curves, which are central objects in this field. Learn about the study of rational points on varieties and the techniques used to determine their existence and properties. Discover the program's focus on understanding both theoretical and computational aspects of determining K-rational points on modular curves XH(K) for various fields and subgroups. This lecture is part of a broader initiative to bring together experts in arithmetic geometry, fostering idea exchange and promoting future research in this direction.