Lecturer: P. Gille

Definition of affine group schemes, group actions, representations. Link with Hopf algebras and comodules. Descent, quotients, examples of representable functors (e.g. centralizers, normalizers). Diagonalisable groups and groups of multiplicative type. Grothendieck's theorem of existence of tori locally for Zariski topology, applications. Split subtori, root data, parabolic subgroups, Levi subgroups. Classification of reductive group schemes by cohomology, examples of forms.