On the Tits indices of absolutely almost simple algebraic groups over local and global fields

We present a new, detailed and uniform proof of the validity of those parts of the classification results regarding absolutely almost simple algebraic groups over p-adic and number fields, announced earlier by Tits, which also covers the case of local and global function fields. The main tools used in this paper are Prasad-Rapinchuk's reciprocity law for Tits indices over global fields and also some (new) Hasse principles for homogeneous spaces over global function fields and for forms in characteristic 2. (C) 2022 Elsevier B.V. All rights reserved.