Please use this identifier to cite or link to this item:
http://hdl.handle.net/2445/120989
Title: | Families of orders of quaternion algebras over $\mathbb{Q}$ |
Author: | Miquel Bleier, Alejandro de |
Director/Tutor: | Travesa i Grau, Artur |
Keywords: | Teoria algebraica de nombres Matrius (Matemàtica) Treballs de fi de màster Varietats de Shimura Quaternions Algebraic number theory Matrices Master's theses Shimura varieties Quaternions |
Issue Date: | 28-Jun-2017 |
Abstract: | Every quaternion algebra contains a set of orders, whose understanding would be helping for the Shimura curves theory development. In this master’s thesis, certain parametric families of orders of quaternion algebras over $\mathbb{Q}$ have been defined, and their relationships with Eichler orders have been studied. In particular, for some given quaternion algebras over $\mathbb{Q}$ , we have defined and studied three families of orders $\mathcal{O}$, $\mathcal{O'}$ and $\mathcal{O''}$ , together with a maximal order $\mathcal{O}^{max}$ belonging to all of the families. As a main result, given a square-free integer $N$ coprime with the discriminant of the quaternion algebra given, it is possible to find an Eichler order of level $N$ belonging to the family $\mathcal{O'}$ and satisfying $\mathcal{O}^{max} \supset \mathcal{O'} \supset \mathcal{O''} \supset \mathcal{O}=\mathbb{Z}+N\mathcal{O}^{max}$, in a way that every quotient is isomorphic to $\mathbb{Z}/N\mathbb{Z}$ as abelian groups, this is, $\mathcla{O}/\mathcal{O'}\cong \mathcla{O'}/\mathcal{O''}\cong \mathcla{O''}/\mathcal{O}\cong\mathbb{Z}/N\mathbb{Z}$. |
Note: | Treballs finals del Màster en Matemàtica Avançada, Facultat de matemàtiques, Universitat de Barcelona, Any: Alejandro de Miquel Bleier, Director: Artur Travesa i Grau |
URI: | http://hdl.handle.net/2445/120989 |
Appears in Collections: | Màster Oficial - Matemàtica Avançada |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
memoria.pdf | Memòria | 273.46 kB | Adobe PDF | View/Open |
This item is licensed under a Creative Commons License