Seminar format: The seminar will take place at the indicated time in video-conference via Zoom. Details will be posted on the Moodle page of the seminar in due time.
Tentative program: The seminar gives an introduction to the arithmetic theory of elliptic curves. Special attention will be given to the arithmetic invariants of an elliptic curve defined over a number field, such as its group of rational points, its Selmer group and its Shafarevich-Tate group. The main goal is to prove the Mordell-Weil theorem on the finite generation of the group of rational points.
J. Silverman, J. Tate, Rational points on elliptic curves, Springer-Verlag.
J. Silverman, The arithmetic of elliptic curves, 2nd edition, Springer-Verlag.