Reference : On modular forms and the inverse Galois problem
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
On modular forms and the inverse Galois problem
Dieulefait, Luis [> >]
Wiese, Gabor mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Transactions of the American Mathematical Society
Yes (verified by ORBilu)
[en] 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 PSL_2(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 good-dihedral primes. Particular care is taken in order to exclude nontrivial inner twists.
2806684 (2012k:11069)

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