Seminar Algebra and Geometry: Mathieu Huruguen (EPFL, Lausanne)

Special reductive groups over an arbitrary field

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 the classification of special reductive groups over an arbitrary field. If time permits, I will give an application to a conjecture of Serre.

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