Speaker：Qing Liu (University of Bordeaux)

Time：2025-10-29 10:00

Location：Conference Room S204 at Experiment Building at Haiyun Campus

Abstract:

Birch and Swinnerton-Dyer's conjecture predicts a precise relation between the L-function of an elliptic curve over the rational numbers and some arithmetic invariants of the elliptic curve. This conjecture has a generalized version for abelian varieties over number fields. For abelian varieties which are Jacobians of curves, some of the corresponding invariants can be read from the curves. In this talk I will explain how this is done "concretely". For hyperelliptic curves, there are even computer program determining these invariants away from the prime 2. I will describe an algorithm for the prime 2.