Th\'eorie de Bruhat-Tits pour les groupes quasi-r\'eductifs

João Lourenço

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arXiv · 2001.05362

Th\'eorie de Bruhat-Tits pour les groupes quasi-r\'eductifs

João Lourenço

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Abstract

We extend (scheme-theoretic) Bruhat-Tits theory to quasi-reductive groups i.e. with trivial split unipotent radical over discretely valued henselian non-archimedean fields $K$, whose ring of integers is excellent and residue field is perfect, building on Bruhat-Tits I et II and the classification of pseudo-reductive groups by Conrad-Gabber-Prasad. The buildings had been constructed previously by Solleveld in a different manner, but they ultimately coincide with ours. We were motivated by the geometry of affine Grassmannians and give some applications at the end (compare also with previously submitted work arXiv:1912.11918).

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João Lourenço. 2020-01-15. Th\'eorie de Bruhat-Tits pour les groupes quasi-r\'eductifs. https://arxiv.org/abs/2001.05362

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