Notes on Cohomological Finite Generation for Finite Group Schemes

These are extended notes based on lectures given by Vincent Franjou, Paul Sobaje, Peter Symonds and Antoine Touz\'e at the Master Class on New Developments in Finite Generation of Cohomology that took place at Bielefeld University in September 2023. Their aim to give a panoramic overview of van der Kallen's recent result on the finite generation of cohomology for finite group schemes over an arbitrary Noetherian base, bringing together the many papers that this theorem relies on, and supplying the necessary background and exposition.