A factorisation ZBK= (0,∞) ⊗ (0,∞) of Beilinson-Kato's system | Vidéo | Carmin.tv

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A factorisation ZBK= (0,∞) ⊗ (0,∞) of Beilinson-Kato's system

By Pierre Colmez

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.

Information about the video

Date of recording 6/20/22
Date of publication 7/25/22
Institution CIRM
Licence CC BY NC ND
Language English
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19934703
Cite this video Colmez Pierre (6/20/22). A factorisation ZBK= (0,∞) ⊗ (0,∞) of Beilinson-Kato's system. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19934703
URL https://dx.doi.org/10.24350/CIRM.V.19934703

Domain(s)

Number Theory

Bibliography

COLMEZ, Pierre et WANG, Shanwen. Une factorisation du syst\eme de Beilinson-Kato. arXiv preprint arXiv:2104.09200, 2021. - https://doi.org/10.48550/arXiv.2104.09200

MSC codes

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