Large images for Galois representations attached to generic modular forms

Abstract

[en] The aim of this project is to study a theorem of Ribet stating that the images of the Galois representations attached to modular forms without Complex Multiplication are large for almost every prime. Firstly, the needed background is introduced in the form of some definitions and basic properties of modular forms and Galois representations. Later, the subgroup classification of general linear groups over finite fields is presented, as well as other useful results from group theory. Finally, Ribet’s theorem is stated and proved using all the tools from algebraic number theory and group theory developed in the previous chapters.