Deformations of certain reducible Galois representations, II

• Autores: Spencer Hamblen, Ravi Ramakrishna
• Localización: American journal of mathematics, ISSN 0002-9327, Vol. 130, Nº 4, 2008, págs. 913-944
• Idioma: inglés
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• Resumen

  • We examine the deformation theory of two dimensional mod $p$ reducible indecomposable Galois representations, removing or relaxing many of the hypotheses of part I. We are able to prescribe local conditions on our deformations by allowing ramification at a set of primes congruent to 1 mod $p$, not 1 mod $p^2$, and satisfying some other splitting conditions. The new hypotheses admit irreducible ordinary characteristic zero lifts of many mod $p$ representations, which by Skinner-Wiles allows us to conclude the modularity of such representations.