Almost split Kac–Moody groups over ultrametric fields

Abstract

For a split Kac-Moody group G over an ultrametric field K, S. Gaussent and the author defined an ordered affine hovel on which the group acts; it generalizes the Bruhat-Tits building which corresponds to the case when G is reductive. This construction was generalized by C. Charignon to the almost split case when K is a local field. We explain here these constructions with more details and prove many new properties e.g. that the hovel of an almost split Kac-Moody group is an ordered affine hovel, as defined in a previous article.