ICTS:31864

Video URL

Bloch-Kato conjecture for CM modular forms and Rankin-Selberg convolutions (Online)

Bloch-Kato conjecture for CM modular forms and Rankin-Selberg convolutions (Online)

(2025). Bloch-Kato conjecture for CM modular forms and Rankin-Selberg convolutions (Online). SciVideos. https://youtube.com/live/XwHC_Hd7EiQ

Bloch-Kato conjecture for CM modular forms and Rankin-Selberg convolutions (Online). SciVideos, May. 29, 2025, https://youtube.com/live/XwHC_Hd7EiQ 

          @misc{ scivideos_ICTS:31864,
            doi = {},
            url = {https://youtube.com/live/XwHC_Hd7EiQ},
            author = {},
            keywords = {},
            language = {en},
            title = {Bloch-Kato conjecture for CM modular forms and Rankin-Selberg convolutions (Online)},
            publisher = {},
            year = {2025},
            month = {may},
            note = {ICTS:31864 see, \url{https://scivideos.org/icts-tifr/31864}}
          }
Francesc Castella
Talk numberICTS:31864
Source RepositoryICTS-TIFR

Abstract

Let E/F be an elliptic curve with CM by an imaginary quadratic field K, and assume that the extension of F generated by the torsion points of E is abelian over K. In this talk I will outline the proof of the p-part of the Birch-Swinnerton-Dyer formula for E in analytic rank 1 for primes p>3 of ordinary reduction. For F=Q, this was originally proved by Rubin in 1991 as a consequence of his proof of the Iwasawa main conjecture for K. In contrast, our approach to the problem is based on the study of an auxiliary Rankin-Selberg convolution, and extends to CM abelian varieties A/K and higher weight CM modular forms.