Geometry and Physics Seminar: Mathieu Huruguen

A linear algebraic group G defined over a field k is called special if every G-torsor over every field extension of k is trivial. In a modern language, it can be shown that the special groups are those of essential dimension zero. In 1958 Grothendieck classified special groups in the case where the base field k is algebraically closed. In this talk I will explain some recent progress towards the classification of special reductive groups over an arbitrary field. In particular, I will give the classification of special semisimple groups, special reductive groups of inner type and special quasisplit reductive groups over an arbitrary field k.