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arXiv · 2310.16396

The Residually Indistinguishable Case of Ribet's Method for GL2

Samit Dasgupta·Mahesh Kakde·Jesse Silliman·Jiuya Wang
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Abstract

Ribet's method provides a strategy for constructing a nontrivial extension of a $p$-adic Galois representation $\rho_1$ by another such representation $\rho_2$. Suppose we are working over a local ring. An important assumption that occurs throughout literature is that the representations $\rho_i$ are residually distinguishable i.e. are residually non-isomorphic. The main theorem of this paper is a general version of Ribet's Lemma for $\rm{GL}_2$ where we do not impose the assumption that the associated characters are residually distinguished.

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Samit Dasgupta, Mahesh Kakde, Jesse Silliman, Jiuya Wang. 2023-10-25. The Residually Indistinguishable Case of Ribet's Method for GL2. https://arxiv.org/abs/2310.16396

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