Student AG Seminar: Morita equivalence of algebraic stacks and flat families of Hopf algebras

Classifying small rank finite group schemes over a field of positive characteristic is a hard problem, and not much less difficult than classifying small rank Hopf algebras in general. By adopting the language of moduli, we can try to make sense of certain invariants defined on certain closed stratum of rank $n$ Hopf algebras. In doing so we will generate interesting examples of Morita equivalent algebraic stacks.