UNCE / SCI / 022
Project seminar 8.March 2023, 14.00, K3
Mentzelos Melistas (CUNI)
A divisibility related to the Birch and Swinnerton-Dyer conjecture
The Birch and Swinnerton-Dyer (BSD) conjecture asserts that the size of the group of rational points of an elliptic curve, as well as several other invariants, are related to the behavior of an associated analytic object, the L-function of the curve. After discussing the BSD conjecture for elliptic curves over the rationals, I will focus on the analytic rank zero case and discuss a conjecture of Agashe, which is a consequence of the BSD. I will then present a theorem that proves Agashe's conjecture. Time permitting I will also talk about more recent work of mine, where a problem of similar flavor is solved for semi-stable elliptic curves.
The seminar will take place within the
Number theory seminar.