New preprint out now: Tits p-indexes of algebraic groups, joint with Charles De Clercq. We give a `localized at a prime p‘ version of the results in Jacques Tits‘s classic 1966 paper Classification of semisimple algebraic groups. In that paper, he introduced the index of a semisimple group and classified all the possible values it can take (up to some questions marks which were later resolved). In our paper, we address the same issue but under the additional hypothesis that every finite extension of the field has degree a power of p, and we give stronger conclusions for exceptional groups.

The p-indexes importance comes from the main result of a previous paper by De Clercq, which gives a necessary and sufficient criterion in terms of the p-indexes of two groups in order for their twisted flag varieties to have the same Chow motives with coefficients in the finite field GF(p).