Rational Conjugacy Classes of Maximal Tori In Groups of Type $D_n$

Abstract

We give a concrete characterization of the rational conjugacy classes of maximal tori in groups of type $D_n$, 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 $D_4$.

References in corpus (2)

• Local-global principles for embedding of fields with involution into simple algebras with involution
• Embeddings of maximal tori in classical groups and explicit Brauer-Manin obstruction

Cited by in corpus (1)

• Embeddings of maximal tori in groups of type $F_4$