Gespeichert in:
| 1. Verfasser: | |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2512.21249 |
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Inhaltsangabe:
- In this article, we study the Zariski closure of modular points in the two-dimensional universal deformation space when the residual Galois representation is reducible. Unlike the previous approaches in the residually irreducible case from Gouvêa-Mazur, Böckle and Allen, our method relies on local-global compatibility results, potential pro-modularity arguments and a non-ordinary finiteness result between the local deformation ring at $p$ and the global deformation ring. This allows us to construct sufficiently many non-ordinary regular de Rham points whose modularity is guaranteed by the recent progress on the Fontaine-Mazur conjecture. Also, we will discuss some applications of our main results, including the equidimensionality of certain big Hecke algebras and big $R=\mathbb{T}$ theorems in the residually reducible case.