Title: The Eisenstein ideal in the theory of modular curves
Date: Friday, October 30, 2020
Place and Time: Zoom, 3:35-4:25 pm
Abstract. Elliptic curves have been studied since antiquity. The arithmetic theories of modular curves and elliptic curves have been intertwined at least since the work of Beppo Levi (1875-1961). Mazur's celebrated article "Modular curves and the Eisenstein ideal" (1977) settled outstanding problems and introduced new tools in both theories. In my talk, I will review some history of the subject and explain how the Eisenstein ideal offers a useful perspective in the study of the group of rational torsion points of the Jacobian of a modular curve.