Potential automorphy of GSpin2n+1-valued Galois representations

We prove a potential automorphy theorem for suitable Galois representations Gamma(F+) -> GSpin(2n+1)(F-p) and Gamma(F+) -> GSpin(2n+1)(Q(p)), where Gamma(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 Gamma(F+) -> GSpin(2n+1)(Q(p)) into compatible systems of GSpin(2n+1)(Q(l))-valued representations.

Automated summary

In this paper, we prove a potential automorphy theorem for suitable Galois representations and also investigate results on solvable descent, enabling us to put representations into compatible systems.