Exotic groups using twisted and mixed group schemes
24 februari 2017
UAntwerpen, Campus Middelheim, G.005 - Middelheimlaan 1 - 2020 Antwerpen (route: UAntwerpen, Campus Middelheim
Seminar by Karsten Naert
About the seminar
We provide a framework which connects three interesting classes of groups: the twisted groups (also known as Suzuki-Ree groups), the mixed groups and the exotic pseudo-reductive 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. The twisted Chevalley groups ^2mathsf B_2, ^2mathsf G_2 and ^2mathsf F_4 arise as rational points of twisted group schemes. The mixed groups in the sense of Tits arise as rational points of mixed group schemes.
The exotic pseudo-reductive groups of Conrad, Gabber and Prasad are Weil restrictions of mixed group schemes. We approach the problem by studying a category with an endomorphism of the identity functor; these results are then applied to the category of schemes in characteristic p, together with the absolute Frobenius.