Automorphic lifts of prescribed types

Details Automorphic lifts of prescribed types Automorphic lifts of prescribed types

2008-10-10

arxiv.org/abs/0810.1877v2

Mathematics

Number Theory

Essentially final version, to appear in Math Annalen. This version does not incorporate any minor changes (e.g. typographical

Scientific paper

We prove a variety of results on the existence of automorphic Galois representations lifting a residual automorphic Galois representation. We prove a result on the structure of deformation rings of local Galois representations, and deduce from this and the method of Khare and Wintenberger a result on the existence of modular lifts of specified type for Galois representations corresponding to Hilbert modular forms of parallel weight 2. We discuss some conjectures on the weights of $n$-dimensional mod $p$ Galois representations. Finally, we use recent work of Taylor to prove level raising and lowering results for $n$-dimensional automorphic Galois representations.

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