4 citations · 4 across the 13 of their papers we have counts for
14 papers
A quotient of the Bruhat-Tits building classifying maximal matrix orders over curves
Luis Arenas-Carmona, Claudio Bravo, Ignacio Saavedra
In a previous work, we defined a quotient graph of the Bruhat-Tits tree associated to the degree two special linear group over a local field whose vertex set is in correspondence w…
On some Diophantine and Ergodic properties of the Schneider map over function fields
Matias Alvarado, Nicolás Arévalo-Hurtado, Claudio Bravo
We introduce and study continued fractions defined by Schneider-like maps over polynomial rings, where the maps are associated with a fixed polynomial of arbitrary degree. In parti…
Computing quaternionic representations via twisted forms of Bruhat-Tits trees
Luis Arenas-Carmona, Claudio Bravo
This work is devoted to the study of representations of finite subgroups of the group of units of quaternion division algebras over a global or local field arising from the inclusi…
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…
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…
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…
Arithmetic subgroups of Chevalley group schemes over function fields II: Conjugacy classes of maximal unipotent subgroups
Claudio Bravo, Benoit Loisel
Let be a smooth, projective, geometrically integral curve defined over a perfect field . Let be the function field of $\mathca…
Relative homology of arithmetic subgroups of
Claudio Bravo
Let be a smooth, projective and geometrically integral curve defined over a finite field . Let be the ring of function of that are regul…
Arithmetic subgroups of Chevalley group schemes over function fields I: quotients of the Bruhat-Tits building by -arithmetic subgroups
Claudio Bravo, Benoit Loisel
Let be a reductive Chevalley group scheme (defined over ). Let be a smooth, projective, geometrically integral curve over a field $\mathbb{F}…
Quotients of the Bruhat-Tits tree by function field analogs of the Hecke congruence subgroups
Claudio Bravo
Let C be a smooth, projective and geometrically integral curve defined over a finite field F. For each closed point P of C, let R be the ring of functions that are regular outside…
Quotients of the Bruhat-Tits tree by arithmetic subgroups of special unitary groups
Luis Arenas-Carmona, Claudio Bravo, Benoit Loisel +1
Let be the function field of a curve over a field of either odd or zero characteristic. Following the work by Serre and Mason on , we study the…
Branches in the Bruhat-Tits tree for local fields of even characteristic
Luis Arenas-Carmona, Claudio Bravo
We extend our previous computations for the relative positions of branches of quaternions to the case of local fields of even characteristic. This is a key step to understand the s…
On genera containing non-split Eichler orders over function fields
Luis Arenas-Carmona, Claudio Bravo
Grothendieck-Birkhoff Theorem states that every finite dimensional vector bundle over the projective line P1 splits as the sum of one dimensional vector bundles. This can be rephra…
On the missing branches of the Bruhat-Tits tree
Luis Arenas-Carmona, Claudio Bravo
Let k be a local field and let A be the two-by-two matrix algebra over k. In our previous work we developed a theory that allows the computation of the set of maximal orders in A c…