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On a lemma of Ribet. (A propos d’un lemme de Ribet.) (French) Zbl 1048.20032
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 K. A. Ribet [Invent. Math. 34, 151-162 (1976; Zbl 0338.12003)].

20G25 Linear algebraic groups over local fields and their integers
20G05 Representation theory for linear algebraic groups