Title:

On modular forms and the inverse Galois problem

Author:

Dieulefait, L. V. (Luis Victor); Wiese, Gabor

Other authors:

Universitat de Barcelona 
Abstract:

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 $ \mathrm{PSL}_2(\mathbb{F}_{p^n})$ occurs as the Galois group of some finite extension of the rational numbers. These groups are obtained as projective images of residual modular Galois representations. Moreover, families of modular forms are constructed such that the images of all their residual Galois representations are as large as a priori possible. Both results essentially use Khare's and Wintenberger's notion of gooddihedral primes. Particular care is taken in order to exclude nontrivial inner twists. 
Subject(s):

Grups discontinus Formes automòrfiques Teoria de nombres Discontinuous groups Automorphic forms Number theory 
Rights:

(c) American Mathematical Society (AMS), 2011

Document type:

Article info:eurepo/semantics/publishedVersion 
Published by:

American Mathematical Society (AMS)

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