Masures associated with split Kac--Moody groups over valued fields

Abstract

Masures are generalizations of Bruhat-Tits buildings adapted to the study of Kac--Moody groups over valued fields. They were introduced by Gaussent and Rousseau in 2007. Rousseau defined an axiomatic for these object and we simplified it. In this paper, which is mainly expository, we construct the masure associated with a split Kac--Moody group over a valued field, and we prove that it satisfies our axiomatic.