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arXiv · 0912.0442

Structures immobili\`eres pour un groupe de Kac-Moody sur un corps local

Cyril Charignon
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Abstract

In this study, we try to generalize Bruhat-Tits's theory to the case of a Kac-Moody group, that is to define an affine building for a Kac-Moody group over a local field. Actually, we will obtain a geometric space wich lacks some of the incidence properties of a building, so that it is called a hovel, following Guy Rousseau's terminology. Hovels have already been obtained for split Kac-Moody groups by Guy Rousseau and St\'ephane Gaussent; here we define them for any group with a (generalized) valuated root datum, a situation wich contains the Kac-Moody groups over local fields, split and nearly split.

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Cyril Charignon. 2009-12-02. Structures immobili\`eres pour un groupe de Kac-Moody sur un corps local. https://arxiv.org/abs/0912.0442

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