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

TL;DR

This paper extends the geometric theory of buildings to Kac-Moody groups over local fields, introducing 'hovels' as a generalization that encompasses split and nearly split cases, broadening the understanding of their geometric structures.

Contribution

It defines hovels for any group with a generalized valuated root datum, generalizing previous constructions for split Kac-Moody groups over local fields.

Findings

Introduced the concept of hovels for Kac-Moody groups over local fields.

Extended the geometric framework beyond split cases.

Provided a new geometric space with properties similar to buildings.

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.