Abstract
In this note we realize seven small simple groups as Galois groups over Q. The technique that we employ is the determination of the images of Galois representations attached to modular and automorphic forms, relying in two cases on recent results of Scholze on the existence of Galois representations attached to non-selfdual automorphic forms.
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
Reference13 articles.
1. Inverse Galois Problem for Small Simple Groups
http://pi.math.cornell.edu/~zywina/papers/smallGalois.pdf
2. Formes Modulaires et Représentations l-adiques;Deligne,1971
3. The weight in Serre's conjectures on modular forms
4. Galois Representations Attached to Eigenforms with Nebentypus;Ribet,1977
5. on l-adic representations attached to modular forms II