Tits indices over semilocal rings

Abstract

We give a simplified proof of Tits' classification of semisimple algebraic groups that remains valid over semilocal rings. In particular, we provide explicit necessary and sufficient conditions that anisotropic groups of a given type appear as anisotropic kernels of semisimple groups of a given Tits index. We also give a new proof of the existence of all indices of exceptional inner type using the notion of canonical dimension of projective homogeneous varieties.

arXiv commentan existence proof added; 29 pages

References in corpus (1)

• Structurable algebras and groups of type E_6 and E_7

Cited by in corpus (3)

• Embedding functors and their arithmetic properties
• Grothendieck-Serre conjecture for adjoint groups of types E_6 and E_7 and for certain classical groups
• Grothendieck-Serre conjecture for groups of type F_4 with trivial f_3 invariant