Special reductive groups over an arbitrary field

2014/03/18 by Mathieu Huruguen, Huruguen, Mathieu · 2 citations
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.1403.4348

21 pages. Comments welcome

arxiv created 2014/03/18 · arxiv updated 2014/03/19

Abstract

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 1958 Grothendieck classified special groups in the case where the base field is algebraically closed. In this paper we describe the derived subgroup and the coradical of a special reductive group over an arbitrary field k. We also classify special semisimple groups, special reductive groups of inner type and special quasisplit reductive groups over an arbitrary field k.

Cited by

• Finite abelian subgroups of algebraic groups
• Classifying torsors of tori with Brauer groups

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