Level lowering modulo prime powers and twisted Fermat equations (Q2882885)

The authors extend the classical concept of level lowering modulo prime numbers as developed by \textit{K. A. Ribet} [Invent. Math. 100, No.2, 431--476 (1990; Zbl 0773.11039)] and others to level lowering modulo powers of primes. Building on work of \textit{E. Halberstadt} and \textit{A. Kraus} [J. Reine Angew. Math. 548, 167--234 (2002; Zbl 1125.11038)] the authors can use their level-lowering result to show the non-solvability of certain twisted Fermat curves, e.g. \(5^2 x^n+ 2^4y^n+ 23^4z^n = 0\) in the case \(n>3\) and \(xyz\neq 0.\) The case \(n=9\) is the one, where the new level-lowering result finds an application.