AI 中文总结
该研究在亏格为二的西格尔模形式下，证明极小模性提升定理，剩余表示源于稳定吉田提升。基于\(R = \mathbb{T}\)定理，建立通用极小普通伽罗瓦变形环自由性及希达族唯一性。
AI 中文摘要
我们在亏格为二的西格尔模形式的情形下证明了一个极小模性提升定理（在热内斯蒂耶 - 蒂卢瓦内和皮洛尼的精神下），当剩余表示源自一个稳定的吉田提升时，即一个实二次域上近乎普通的希尔伯特模特征尖形式的自守诱导。作为基础的\(R = \mathbb{T}\)定理的应用，我们建立了一个在双变量伊瓦萨瓦代数上的通用极小普通伽罗瓦变形环的自由性，以及通过具有非常正则权重的经典\(p\)-普通西格尔模特征形式的希达族的唯一性。
英文摘要
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.
Comments28 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
