Relative deformation theory, relative Selmer groups, and lifting irreducible Galois representations

Najmuddin Fakhruddin; Chandrashekhar Khare; Stefan Patrikis

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arXiv · 1904.02374

Relative deformation theory, relative Selmer groups, and lifting irreducible Galois representations

Najmuddin Fakhruddin·Chandrashekhar Khare·Stefan Patrikis

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Abstract

We study irreducible odd mod $p$ Galois representations $\barρ \colon \mathrm{Gal}(\overline{F}/F) \to G(\overline{\mathbb{F}}_p)$, for $F$ a totally real number field and $G$ a general reductive group. For $p \gg_{G, F} 0$, we show that any $\barρ$ that lifts locally, and at places above $p$ to de Rham and Hodge-Tate regular representations, has a geometric $p$-adic lift. We also prove non-geometric lifting results without any oddness assumption.

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Najmuddin Fakhruddin, Chandrashekhar Khare, Stefan Patrikis. 2021-10-15. Relative deformation theory, relative Selmer groups, and lifting irreducible Galois representations. https://arxiv.org/abs/1904.02374

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