Velibor Bojkovic

After recalling the structure of quasi-smooth Berkovich curves (via semistable reduction theorem), we will introduce the basic notions used for studying finite morphisms of such curves, such as different function, property of a morphism to be radial, profile function of a morphism, Herbrand function, Riemann-Hurwitz formula…. we will move on to stating the basic theory of p-adic differential equations on such curves. We will prove the pushforward formula for the change of multiradius of such equations and see how the pushforward of the constant connection is related to the ramification theory of finite morphisms of Berkovich curves. This is a joint work with Jérôme Poineau.