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

Najmuddin Fakhruddin, Chandrashekhar Khare, Stefan Patrikis

We study irreducible odd mod $p$ Galois representations $\bar{\rho }:\mathrm{Gal}(\overline{F}/F)\to G({\overline{\mathbb{F}}}_p)$, for $F$ a totally real number field and $G$ a ge…