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arXiv · 0908.2577

Can an anisotropic reductive group admit a Tits system?

Pierre-Emmanuel Caprace·Timothée Marquis
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Abstract

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 may 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.

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Pierre-Emmanuel Caprace, Timothée Marquis. 2009-08-18. Can an anisotropic reductive group admit a Tits system?. https://doi.org/10.4310/pamq.2011.v7.n3.a3

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