Compatible systems of symplectic Galois representations and the inverse Galois problem I. Images of projective representations

@article{AriasdeReyna2012CompatibleSO,
  title={Compatible systems of symplectic Galois representations and the inverse Galois problem I. Images of projective representations},
  author={Sara Arias-de-Reyna and Luis V. Dieulefait and Gabor Wiese},
  journal={Transactions of the American Mathematical Society},
  year={2012},
  volume={369},
  pages={887-908}
}
This article is the first part of a series of three articles about compatible systems of symplectic Galois representations and applications to the inverse Galois problem. In this first part, we determine the smallest field over which the projectivisation of a given symplectic group representation satisfying some natural conditions can be defined. The answer only depends on inner twists. We apply this to the residual representations of a compatible system of symplectic Galois representations… 
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