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math.GR2024
Tessellations of an affine apartment by affine weight polytopes
Claudio Bravo, Auguste Hébert, Diego Izquierdo +1
Let $\A$ be a finite dimensional vector space and be a finite root system in $\A$. To this data is associated an affine poly-simplicial complex. Motivated by a forthcoming cons…
math.NT2024
A Continued Fractions Theory for the completion of the Puiseux field
Luis Arenas-Carmona, Claudio Bravo
In this work, we study a continued fractions theory for the topological completion of the field of Puiseux series. As usual, we prove that any element in the completion can be deve…
math.NT2024
Diophantine Approximation in local function fields via Bruhat-Tit trees
Luis Arenas-Carmona, Claudio Bravo
We use the theory of arithmetic quotients of the Bruhat-Tits tree developed by Serre and others to obtain Dirichlet-style theorems for Diophantine approximation on global function…