On Modular Forms and the Inverse Galois Problem

Details On Modular Forms and the Inverse Galois Problem On Modular Forms and the Inverse Galois Problem

2009-05-08

arxiv.org/abs/0905.1288v1

Mathematics

Number Theory

17 pages

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

On Modular Forms and the Inverse Galois Problem does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On Modular Forms and the Inverse Galois Problem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On Modular Forms and the Inverse Galois Problem will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-703965