Higher Tits indices of algebraic groups

Details Higher Tits indices of algebraic groups Higher Tits indices of algebraic groups

2007-06-19

arxiv.org/abs/0706.2827v3

Mathematics

Algebraic Geometry

29 pages, Appendix by Mathieu Florence

Scientific paper

Let G be a semisimple algebraic group over a field k. We introduce the higher Tits indices of G as the set of all Tits indices of G over all field extensions K/k. In the context of quadratic forms this notion coincides with the notion of the higher Witt indices introduced by M. Knebusch and classified by N. Karpenko and A. Vishik. We classify the higher Tits indices for exceptional algebraic groups. Our main tools involve the Chow groups and the Chow motives of projective homogeneous varieties, Steenrod operations, and the notion of the J-invariant of algebraic groups.

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