Philippe.Gille@math.u-psud.fr

Submission: 2003, Jul 8

Let $G/k$ be a semisimple algebraic group defined over a field $k$ with separable closure $k_s$. Let $T$ a maximal $k$--torus of $G$. The Galois action on the root system $\Phi( G_{k_s}, T_{k_s})$ provides an invariant in Galois cohomology, we call it the type of $T$ in $G$. We show that all possible type occur for maximal tori of quasi-split semisimple groups.

2000 Mathematics Subject Classification: 20G15

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