Lifting irreducible Galois representations

Najmuddin Fakhruddin; Chandrashekhar Khare; Stefan Patrikis

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arXiv · 1810.05803

Lifting irreducible Galois representations

Najmuddin Fakhruddin·Chandrashekhar Khare·Stefan Patrikis

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Abstract

We study irreducible mod p representations, valued in general reductive groups, of the Galois group of a number field. When the number field is totally real, we show that odd representations satisfying local ramification hypotheses and a certain multiplicity-free condition on the adjoint representation admit geometric lifts. For general number fields, we show without any oddness or multiplicity condition that the representation admits a p-adic lift if it does everywhere locally.

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Najmuddin Fakhruddin, Chandrashekhar Khare, Stefan Patrikis. 2018-10-13. Lifting irreducible Galois representations. https://arxiv.org/abs/1810.05803

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