A minimal modularity lifting theorem for Siegel modular forms

Shaunak V. Deo; Bharathwaj Palvannan

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arXiv · 2607.13100

A minimal modularity lifting theorem for Siegel modular forms

Shaunak V. Deo·Bharathwaj Palvannan

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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 $R=\mathbb{T}$ 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 $p$-ordinary Siegel modular eigenforms with very regular weights.

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Shaunak V. Deo, Bharathwaj Palvannan. 2026-07-14. A minimal modularity lifting theorem for Siegel modular forms. https://arxiv.org/abs/2607.13100

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