Year: 2023
Type: preprint
Abstract: Ribet's method provides a strategy for constructing a nontrivial extension of a $p$-adic Galois representation $ρ_1$ by another such representation $ρ_2$. Suppose we are working over a local ring. An important assumption that occurs throughout literature is that the representations $ρ_i$ 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.
Source: arXiv (Cornell University)
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4388005595