Under standard Taylor-Wiles hypotheses, every irreducible 2-dimensional totally odd mod p Galois representation of the absolute Galois group of a totally real field F admits lifts on arbitrary prescribed components of local deformation rings, allowing potentially semistable conditions with arbitrary
and Thorne, Jack A
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Prescribed lifts of 2-dimensional representations
Under standard Taylor-Wiles hypotheses, every irreducible 2-dimensional totally odd mod p Galois representation of the absolute Galois group of a totally real field F admits lifts on arbitrary prescribed components of local deformation rings, allowing potentially semistable conditions with arbitrary