Rational conjugacy classes of maximal tori in groups of Dn

Abstract

We give a concrete characterization of the rational conjugacy classes of maximal tori in groups of type Dn, with specific emphasis on the case of number fields and p-adic fields. This includes the forms associated to quadratic spaces, all of their inner and outer forms as well as the Spin groups, their simply connected covers. In particular, in this work, we handle all (simply connected) outer forms of D4.