# 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…

## 7 Citations

Compatible systems of symplectic Galois representations and the inverse Galois problem

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Abstract In this note, we give a self-contained proof of the following classification (up to conjugation) of finite subgroups of GSpn(F̅ℓ) containing a nontrivial transvection for ℓ ≥ 5, which can be…

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In the 80's Aschbacher classified the maximal subgroups of almost all of the finite almost simple classical groups. Essentially, this classification divide these subgroups into two types. The first…

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In this paper we construct families of Hilbert modular newforms without exceptional primes. This is achieved by generalizing the notion of good-dihedral primes, introduced by Khare and Wintenberger…

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Compatible systems of symplectic Galois representations and the inverse Galois problem III. Automorphic construction of compatible systems with suitable local properties

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This article is the third and last part of a series of three articles about compatible systems of symplectic Galois representations and applications to the inverse Galois problem. This part proves…

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