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....
Line bundles on moduli spaces/stacks of G-bundles were studied intensively in 90’s by many mathematicians including Beauville, Laszlo, Sorger, Faltings, Kumar, Narasimhan, Teleman, etc. The main problems are the Verlinde formula for the dimension of global sections of these line bundles, and the determination of the Picard groups of the moduli spaces/stack of G-bundles.In this talk, I will dis...