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

TL;DR

This paper constructs and verifies the axiomatic properties of masures, a generalization of Bruhat-Tits buildings, for split Kac--Moody groups over valued fields, simplifying previous axiomatic definitions.

Contribution

It provides a simplified axiomatic framework and constructs masures for split Kac--Moody groups over valued fields, mainly in an expository manner.

Findings

Constructed masures for split Kac--Moody groups over valued fields.

Proved that these masures satisfy the simplified axiomatic.

Clarified the relationship between masures and Bruhat-Tits buildings.

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.