Appears in collection : Galois Representations, Automorphic Forms and L-Functions / Représentations galoisiennes, formes automorphes et leurs fonctions L
I will discuss recent joint work with Sarah Zerbes in which we use Euler systems and reciprocity laws for GSp(4) to study the analytic rank 0 case of the Birch--Swinnerton-Dyer conjecture for abelian surfaces. Via restriction of scalars, this also includes the BSD conjecture for analytic rank 0 elliptic curves over imaginary quadratic fields. Our main result is a conditional proof of the conjecture subject to an assumption about the local geometry of the GSp4 eigenvariety at non-regular-weight points. I will explain how this conjecture arises and some motivation for why it seems plausible that it should hold.
By Alain Connes
By Javier Fresán
![[1237] Moments de fonctions et $L$ stabilité homologique](/media/cache/video_light/uploads/video/Bourbaki.png)
