Functoriality and the inverse Galois problem

@article{Khare2008FunctorialityAT,
  title={Functoriality and the inverse Galois problem},
  author={Chandrashekhar B. Khare and Michael Larsen and Gordan Savin},
  journal={Compositio Mathematica},
  year={2008},
  volume={144},
  pages={541 - 564}
}
Abstract We prove that, for any prime ℓ and any even integer n, there are infinitely many exponents k for which $\mathrm {PSp}_n(\mathbb {F}_{\ell ^k})$ appears as a Galois group over $\mathbb {Q}$. This generalizes a result of Wiese from 2006, which inspired this paper. 
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