A minimal modularity lifting theorem for Siegel modular forms
arXiv:2607.13100
The authors prove a minimal modularity lifting theorem for genus‑2 Siegel modular forms whose residual Galois representation comes from a stable Yoshida lift, and apply the resulting R=𝕋 theorem to study ordinary deformation rings and the uniqueness of Hida families.
Abstract
We prove a minimal modularity lifting theorem (in the spirit of Genestier--Tilouine and Pilloni) in the setting of Siegel modular forms of genus two when the residual representation arises from a stable Yoshida lift, that is, an automorphic induction of a nearly ordinary Hilbert modular eigencuspform over a real quadratic field. As applications of the underlying theorem, we establish the freeness of a universal minimal ordinary Galois deformation ring over an Iwasawa algebra in two variables along with the uniqueness of Hida families passing through classical -ordinary Siegel modular eigenforms with very regular weights.
28 pages, we have moved the modularity lifting theorem from our preprint arXiv:2602.20737v1 to this new manuscript. Comments are welcome! arXiv admin note: text overlap with arXiv:2602.20737