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arXiv · 1710.09272

A new axiomatics for masures

Auguste Hébert
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Abstract

Masures are generalizations of Bruhat-Tits buildings. They were introduced to study Kac-Moody groups over ultrametric fields, which generalize reductive groups over the same fields. If A and A are two apartments in a building, their intersection is convex (as a subset of the finite dimensional affine space A) and there exists an isomorphism from A to A fixing this intersection. We study this question for masures and prove that the analogous statement is true in some particular cases. We deduce a new axiomatic of masures, simpler than the one given by Rousseau.

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Auguste Hébert. 2017-10-25. A new axiomatics for masures. https://doi.org/10.4153/s0008414x19000051

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