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Can an anisotropic reductive group admit a tits system?

par Caprace, Pierre-Emmanuel ;Marquis, Timothée
Référence Pure and Applied Mathematics Quarterly, 7, 3, page (539-557)
Publication Publié, 2011-07

Article révisé par les pairs

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Résumé :

Seeking for a converse to a well-known theorem by Borel-Tits, we address the question whether the group of rational points G(k) of an anisotropic reductive k-group can admit a split spherical BN-pair. We show that if k is a perfect field or a local field, then such a BN-pair must be virtually trivial. We also consider arbitrary compact groups and show that the only abstract BN-pairs they can admit are spherical, and even virtually trivial provided they are split.