Abstract

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.

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 913-944
Launched on MUSE
2008-08-07
Open Access
No
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