4 citations · 9 across the 19 of their papers we have counts for
28 papers
On bass orders in division algebras
Luis Arenas-Carmona
A result by F.-T. Tu dating from 2011 states that the orders in a local matrix algebra of dimension four that can be written as a finite intersection of maximal orders are those ha…
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 representations of Metacyclic groups whose integral forms can be computed from a single residual representation
Bruno Aguiló-Vidal, Luis Arenas-Carmona, Matías Saavedra-Lagos
In a previous work we computed the number of integral forms, over its field of definition, of an irreducible representation of a dihedral group. Here we apply the theory of Bruhat-…
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…
Two dimensional integral representations via branches of the Bruhat-Tits tree
Bruno Aguiló-Vidal, Luis Arenas-Carmona, Matías Saavedra-Lagos
We apply the theory of branches in Bruhat-Tits trees, developed in previous works by the second author and others, to the study of two dimensional representations of finite groups…
Eichler orders, quotient graphs and random walks
Luis Arenas-Carmona, Marco Godoy
We study the extent to which the quotient of the Bruhat-Tits tree at one place , associated to a genus of orders of maximal rank, can be computed from the analogous quotient at…
Two characterizations of Bass orders via branches
Luis Arenas-Carmona
It has been known for some time that the orders in the four dimensional matrix algebra over a local field that can be written as a finite intersection of maximal orders are precise…
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…
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…
Branches on division algebras
Manuel Arenas, Luis Arenas-Carmona
We describe the set of maximal orders in a 2-by-2 matrix algebra over a non-commutative local division algebra B containing a given suborder, for certain important families of such…
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…
Simultaneous diagonalization of vector bundles
Luis Arenas-Carmona
Grothendieck-Birkhoff Theorem states that every finite dimensional vector bundle over the projective line splits as the sum of one dimensional vector bundles. In this work we study…
On optimal embeddings and trees
Manuel Arenas, Luis Arenas-Carmona, Jaime Contreras
We apply the theory of Bruhat-Tits trees to the study of optimal embeddings of two and three dimensional commutative orders into quaternion algebras. Specifically, we determine how…
On some branches of the Bruhat-Tits tree
Luis Arenas-Carmona, Ignacio Saavedra
We give an algorithm to explicitly compute the largest subtree, in the local Bruhat-Tits tree for PSL_2(k), whose vertices correspond to orders containing a given suborder H, in te…
Roots of unity in definite quaternion orders
Luis Arenas-Carmona
A commutative order in a quaternion algebra is called selective if it is embeds into some, but not all, the maximal orders in the algebra. It is known that a given quadratic order…
Selectivity on division algebras
Luis Arenas-Carmona
A commutative order in a central simple algebra over a number field is said to be selective if it embeds in some, but not all, the maximal orders in the algebra. We completely char…
Spinor class field for generalized Eichler orders
Luis Arenas-Carmona
We compute the spinor class field for a genus of orders, in a central simple algebra of higher dimension, that are intersections of two maximal orders. In particular, we compute th…
Representation field for orders of small ranks
Luis Arenas-Carmona
A representation field for a non-maximal order H in a central simple algebra A is a subfield of the spinor class field of maximal orders which determines the set of spinor genera o…
Computing quaternion quotient graphs via representation of orders
Luis Arenas-Carmona
We study the correspondence assigning the vertices of a certain quotient of the local Bruhat-Tits tree for the general linear group over a global function field, to conjugacy class…
Eichler orders, trees and Representation Fields
Luis Arenas-Carmona
If H and D are two orders in a central simple algebra A with D of maximal rank, the representation field F(D|H) is a subfield of the spinor class field of the genus of D which dete…
Maximal selectivity for orders in fields
Luis Arenas-Carmona
If H and D are two orders in a central simple algebra A with D of maximal rank and containing H, the theory of representation fields describes the set of spinor genera of orders in…