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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.
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 the following new result for the inverse Galois pro
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 projectivi
In this paper we generalize results of P. Le Duff to genus n hyperelliptic curves. More precisely, let C/Q be a hyperelliptic genus n curve and let J(C) be the associated Jacobian variety. Assume that there exists a prime p such that J(C) has semista
For each of the groups PSL2(F25), PSL2(F32), PSL2(F49), PGL2(F25), and PGL2(F27), we display the first explicitly known polynomials over Q having that group as Galois group. Each polynomial is related to a Galois representation associated to a modula
Conjecturally, the Galois representations that are attached to essentially selfdual regular algebraic cuspidal automorphic representations are Zariski-dense in a polarized Galois deformation ring. We prove new results in this direction in the context