Automorphic lifts of prescribed types

2008/10/10 by Toby Gee, Gee, Toby · 1 citation
Mathematics · #11F33 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.0810.1877

openalex publication_date 2008/10/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Cited by

• On the finite length of some p-adic representations of the quaternion algebra over \Q_p

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