Potential automorphy of GSpin_2n+1 -valued Galois representations

We prove a potential automorphy theorem for suitable Galois representations Γ _F^+→GSpin_2n+1(𝔽_p) and Γ _F^+→GSpin_2n+1(ℚ_p) , where Γ _F^+ is the absolute Galois group of a totally real field F^+ . We also prove results on solvable descent for GSp_2n(𝔸_F^+) and use these to put representations Γ _F^+→GSpin_2n+1(ℚ_p) into compatible systems of GSpin_2n+1(ℚ_l) -valued representations.