Stefan Reppen: Arithmetic Geometry Learning Seminar - Diophantine problems and p-adic period mappings

Abstract:
We will recall the definition of de Rham cohomology in the complex setting. We will recall the Hodge filtration and the Gauss-Manin connection on de Rham cohomology, and describe how to use this to compare nearby fibers and obtain a period map. We finish by showing that the Zariski closure of the period map around a point contains the orbit of the image of this point under the monodromy action.