The sign of Galois representations attached to automorphic forms for unitary groups

Abstract

We determine the sign of the polarization of any polarized irreducible factor of a Galois representation attached to a polarized cohomological cuspidal automorphic form of Gl_n of a CM field: it is always +1, as was conjectured by Gross.

16 pages

Cited by in corpus (8)

• Deformations of polarized automorphic Galois representations and adjoint Selmer groups
• Galois representations attached to automorphic forms on GL_2 over CM fields
• Minimal modularity lifting for non-regular symplectic representations
• Serre weight conjectures for $p$-adic unitary groups of rank 2
• Galois representations for even general special orthogonal groups
• Smoothness of definite unitary eigenvarieties at critical points
• Globally realizable components of local deformation rings
• Lafforgue pseudocharacters and parities of limits of Galois representations