Wenhan Dai

Instructional Workshop on Iwasawa Theory for Automorphic Forms

Online, Korean Institute for Advanced Study.

Recently, there have been significant progresses in Iwasawa theory for elliptic curves and modular forms. Remarkably, these progresses have important applications to the cerebrated Birch and Swinnerton-Dyer conjecture, one of the Millennium Prize Problems. The main goal of this instructional workshop is to go through many details of the recent work of Castella, Liu, and Wan on the Iwasawa main conjecture for automorphic forms on GU(3,1) (arXiv:2109.08375). In particular, this work plays an important role to establish the Iwasawa main conjecture for a large class of elliptic curves with supersingular reduction.

• Instructor: Francesc Castella (UCSB), Zheng Liu (UCSB), Xin Wan (Morningside Center of Mathematics, CAS).
• Time: December 19-22, 2022.

Contents

1. Francesc Castella’s:
   • (12/19) Some arithmetic applications (notes, video).
   • (12/20) Cuspidal Hida theory for semi-ordinary forms (notes, video).
   • (12/21) Proof of signed main conjectures (notes, video).
2. Zheng Liu’s:
   • (12/20) Non-cuspidal Hida theory for semi-ordinary forms on GU(3,1) (notes, video).
   • (12/21) The construction of Klingen-Eisenstein family and the constant term (notes, video).
   • (12/22) The non-degenerate Fourier-Jacobi coefficients (notes, video).
3. Xin Wan’s: (speaker’s slides)
   • (12/19) Main results and tools (video).
   • (12/20) General strategy (video).
   • (12/22) Lattice construction (video).

Caution: The recoding videos (currently available at Bilibili) are not committed to be permanently available.