The work of Chevalley ([BIBLE], [Chev61]) and Demazure–Grothendieck [SGA3] provides a satisfactory understanding of the reasons for the existence and uniqueness of “Chevalley groups” over Z. These are the reductive group schemes G → Spec(Z) (i.e., smooth affine groups with connected reductive geometric fibers) for which there exists closed subtorus T ⊂ G over Z that is maximal on geometric fibe...
