On a lemma of Ribet.
Let \(R\) be a discrete complete valuation ring, \(K\) its fraction field, \(k\) the residue field, and \(V\) an \(n\)-dimensional \(K\)-vector space. Consider an irreducible representation \(\rho\colon G\to\text{GL}(V)\) of a group \(G\) which stabilizes a lattice \(\Lambda\subset V\); this defines a representation \(\overline\rho\colon G\to\text{GL}(n,k)\). The main result of this paper consists in finding extensions between factors of \(\overline\rho\). The case \(n=2\) is an important lemma of \textit{K. A. Ribet} [Invent. Math. 34, 151-162 (1976; Zbl 0338.12003)].
scientific article; zbMATH DE number 2099240