Tits indices over semilocal rings

Details Tits indices over semilocal rings Tits indices over semilocal rings

2008-07-14

arxiv.org/abs/0807.2140v3

Mathematics

Algebraic Geometry

an existence proof added; 29 pages

Scientific paper

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.

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