Barry Mazur | About the Birch and Swinnerton–Dyer Conjecture скачать в хорошем качестве

Barry Mazur | About the Birch and Swinnerton–Dyer Conjecture

Millennium Prize Problems Lecture 2/4/2026 Speaker: Barry Mazur, Harvard University Title: About the Birch and Swinnerton–Dyer Conjecture Abstract: In the 1950s Bryan Birch and Peter Swinnerton–Dyer made computations that suggested a striking connection between a basic global invariant of an elliptic curve E over the field of rational numbers (namely, the rank of its group of rational points) and certain asymptotics of its local arithmetic invariants (i.e., the number of its rational points over finite fields). This initial observation has evolved into their conjecture. My lecture will be an introduction to the general ideas behind its ever-expanding development.