AbstractIn this presentation, we will discuss the images of Galois representations. In particular, we will address the tame version of the Fontaine-Mazur conjecture, as well as the issue of the existence of Galois extensions with open image.About Christian Maire“Mes domaines d'expertises sont la théorie des nombres, l'arithmétique, l'algèbre sur les corps de nombres, les pro-p extensions, etc....
PrerequisiteBasic commutative algebra, algebraic geometry, algebraic number theoryAbstractThis course is intended to give a gentle introduction to p-adic families of modular forms and p-adic L-functions. We roughly cover the contents of "The Eigenbook" by Belliache. We will start by introducing a general construction of eigenvariety, and discuss modular symbols and their connection to modular f...