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arXiv · 2411.18661

On the pro-modularity in the residually reducible case for some totally real fields

Xinyao Zhang
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Abstract

In this article, we study the relation between the universal deformation rings and big Hecke algebras in the residually reducible case. Following the strategy of Skinner-Wiles and Pan's proof of the Fontaine-Mazur conjecture, we prove a pro-modularity result. Based on this result, we also give a conditional big $R=\mathbb{T}$ theorem over some totally real fields, which is a generalization of Deo's result.

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Xinyao Zhang. 2024-11-27. On the pro-modularity in the residually reducible case for some totally real fields. https://arxiv.org/abs/2411.18661

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