ICTS:31899

Video URL

Degenerate automorphic forms and Euler systems-V (Online)

Degenerate automorphic forms and Euler systems-V (Online)

(2025). Degenerate automorphic forms and Euler systems-V (Online). SciVideos. https://youtube.com/live/ti2kuxPVuno

Degenerate automorphic forms and Euler systems-V (Online). SciVideos, May. 23, 2025, https://youtube.com/live/ti2kuxPVuno 

          @misc{ scivideos_ICTS:31899,
            doi = {},
            url = {https://youtube.com/live/ti2kuxPVuno},
            author = {},
            keywords = {},
            language = {en},
            title = {Degenerate automorphic forms and Euler systems-V (Online)},
            publisher = {},
            year = {2025},
            month = {may},
            note = {ICTS:31899 see, \url{https://scivideos.org/icts-tifr/31899}}
          }
Marco Sangiovanni Vincentelli
Talk numberICTS:31899
Source RepositoryICTS-TIFR

Abstract

Euler Systems have proven to be versatile tools for understanding Selmer groups and their connections to special values of L-functions. However, despite the key role they have played in making progress toward foundational conjectures in number theory like the Birch–Swinnerton-Dyer and Bloch– Kato Conjectures, only a handful of provably non-trivial Euler systems have been constructed to date. A significant obstacle to constructing Euler Systems lies in producing candidate Galois cohomology classes. This lecture series presents a method to overcome this obstacle that does not rely on rare (known) motivic classes. We will focus on building ´etale cohomology classes originating from automorphic data: Eisenstein series and Theta series. This framework not only retrieves most classical Euler systems but can also be applied to construct an Euler system for the adjoint of an elliptic modular form.
References:
• C. Skinner, L-values and nonsplit extensions: a simple case, https://msp.org/ent/2024/3-1/p03.xhtml
• H. Darmon etal, p-adic L-functions and Euler systems: a tale in two trilogies.