Companion forms for unitary and symplectic groups

Abstract

We prove a companion forms theorem for ordinary n-dimensional automorphic Galois representations, by use of automorphy lifting theorems developed by the second author, and a technique for deducing companion forms theorems due to the first author. We deduce results about the possible Serre weights of mod l Galois representations corresponding to automorphic representations on unitary groups. We then use functoriality to prove similar results for automorphic representations of GSp4 over totally real fields.

40 pages

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• Weight elimination in Serre-type conjectures
• Minimal modularity lifting for non-regular symplectic representations
• Companion Forms in Parallel Weight One
• A geometric Jacquet-Langlands correspondence for paramodular Siegel threefolds
• Serre weights for three-dimensional wildly ramified Galois representations