A new axiomatics for masures II

TL;DR

This paper refines the foundational axioms of masures, a generalization of Bruhat-Tits buildings, by proving convexity of apartment intersections and simplifying their axiomatic structure.

Contribution

It introduces a simplified axiomatic framework for masures and proves convexity of apartment intersections, advancing the theoretical understanding of these structures.

Findings

Intersection of two apartments is convex

Simplified axiomatic definition of masures

Enhanced theoretical framework for masures

Abstract

Masures are generalizations of Bruhat-Tits buildings. They were introduced by Gaussent and Rousseau in order to study Kac-Moody groups over valued fields. We prove that the intersection of two apartments of a masure is convex. Using this, we simplify the axiomatic definition of masures given by Rousseau.