Twisting and Mixing
Abstract
We present a framework that connects three interesting classes of groups: the twisted groups (also known as SuzukiRee groups), the mixed groups and the exotic pseudoreductive groups. For a given characteristic p, we construct categories of twisted and mixed schemes. Ordinary schemes are a full subcategory of the mixed schemes. Mixed schemes arise from a twisted scheme by base change, although not every mixed scheme arises this way. The group objects in these categories are called twisted and mixed group schemes. Our main theorems state: (1) The twisted Chevalley groups ${}^2\mathsf B_2$, ${}^2\mathsf G_2$ and ${}^2\mathsf F_4$ arise as rational points of twisted group schemes. (2) The mixed groups in the sense of Tits arise as rational points of mixed group schemes over mixed fields. (3) The exotic pseudoreductive groups of Conrad, Gabber and Prasad are Weil restrictions of mixed group schemes.
 Publication:

arXiv eprints
 Pub Date:
 March 2017
 arXiv:
 arXiv:1703.03794
 Bibcode:
 2017arXiv170303794N
 Keywords:

 Mathematics  Group Theory;
 Mathematics  Algebraic Geometry;
 Mathematics  Category Theory;
 20G15;
 18A05;
 14L15
 EPrint:
 68 pages, comments and suggestions are warmly welcomed