We study irreducible odd mod p Galois representations , for F a totally real number field and G a general reductive group. For , we show that any 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.
In memory of Jean-Pierre Wintenberger, 1954–2019
"Relative deformation theory, relative Selmer groups, and lifting irreducible Galois representations." Duke Math. J. 170 (16) 3505 - 3599, 1 November 2021. https://doi.org/10.1215/00127094-2021-0003