Automorphic Galois representations and the inverse Galois problem

@article{AriasdeReyna2013AutomorphicGR,
  title={Automorphic Galois representations and the inverse Galois problem},
  author={Sara Arias-de-Reyna},
  journal={arXiv: Number Theory},
  year={2013}
}
A strategy to address the inverse Galois problem over Q consists of exploiting the knowledge of Galois representations attached to certain automorphic forms. More precisely, if such forms are carefully chosen, they provide compatible systems of Galois representations satisfying some desired properties, e.g. properties that reflect on the image of the members of the system. In this article we survey some results obtained using this strategy. 
2 Citations
On the images of the Galois representations attached to certain RAESDC automorphic representations of GL n ( A Q )
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
On the images of the Galois representations attached to certain RAESDC automorphic representations of $\mathrm{GL}_n (\mathbb{A}_\mathbb{Q})$
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

References

SHOWING 1-10 OF 45 REFERENCES
Compatible systems of symplectic Galois representations and the inverse Galois problem
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
On modular forms and the inverse Galois problem
In this article new cases of the Inverse Galois Problem are established. The main result is that for a fixed integer n, there is a positive density set of primes p such that PSL2(Fpn) occurs as the
Compatible systems of symplectic Galois representations and the inverse Galois problem I. Images of projective representations
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
An Application of Maeda's Conjecture to the Inverse Galois Problem
It is shown that Maeda’s conjecture on eigenforms of level 1 implies that for every positive even d and every p in a density-one set of primes, the simple group PSL2(Fpd) occurs as the Galois group
Functoriality and the inverse Galois problem
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 $\mathbb {Q}$.
Potential automorphy and change of weight
We prove an automorphy lifting theorem for l-adic representations where we impose a new condition at l, which we call \potentential diagonalizability." This result allows for \change of weight" and
Monodromy of Galois representations and equal-rank subalgebra equivalence
We study l-independence of monodromy groups G_l of any compatible system of l-adic representations (in the sense of Serre) of number field K assuming semisimplicity. We prove that the formal
Maximality of Galois actions for compatible systems
in the sense of Serre [19]. Of course, the image of ρ` is not generally Zariski-dense in GLn(Q`), so the maximality condition must be formulated relative to the Zariski closure, G`, of ρ`(Gal(K/K)).
On projective linear groups over finite fields as Galois groups over the rational numbers
Ideas and techniques from Khare´s and Wintenberger’s preprint on the proof of Serre’s conjecture for odd conductors are used to establish that for a fixed prime l infinitely many of the groups
...
...