Article (Scientific journals)
On modular forms and the inverse Galois problem
Dieulefait, Luis; Wiese, Gabor
2011In Transactions of the American Mathematical Society, 363 (9), p. 4569--4584
Peer reviewed
 

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Abstract :
[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.
Disciplines :
Mathematics
Author, co-author :
Dieulefait, Luis
Wiese, Gabor  ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
Language :
English
Title :
On modular forms and the inverse Galois problem
Publication date :
2011
Journal title :
Transactions of the American Mathematical Society
ISSN :
0002-9947
Volume :
363
Issue :
9
Pages :
4569--4584
Peer reviewed :
Peer reviewed
Commentary :
2806684 (2012k:11069)
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