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| dc.contributor | Travesa i Grau, Artur | |
| dc.creator | Miquel Bleier, Alejandro de | |
| dc.date | 2018-03-22T10:25:36Z | |
| dc.date | 2018-03-22T10:25:36Z | |
| dc.date | 2017-06-28 | |
| dc.date.accessioned | 2024-12-16T10:26:20Z | |
| dc.date.available | 2024-12-16T10:26:20Z | |
| dc.identifier | http://hdl.handle.net/2445/120989 | |
| dc.identifier.uri | http://fima-docencia.ub.edu:8080/xmlui/handle/123456789/20924 | |
| dc.description | Treballs finals del Màster en Matemàtica Avançada, Facultat de matemàtiques, Universitat de Barcelona, Any: Alejandro de Miquel Bleier, Director: Artur Travesa i Grau | |
| dc.description | 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, $\mathcla{O}/\mathcal{O'}\cong \mathcla{O'}/\mathcal{O''}\cong \mathcla{O''}/\mathcal{O}\cong\mathbb{Z}/N\mathbb{Z}$. | |
| dc.format | 29 p. | |
| dc.format | application/pdf | |
| dc.language | eng | |
| dc.rights | cc-by-sa (c) Alejandro de Miquel Bleier, 2017 | |
| dc.rights | http://creativecommons.org/licenses/by-sa/3.0/es/ | |
| dc.rights | info:eu-repo/semantics/openAccess | |
| dc.source | Màster Oficial - Matemàtica Avançada | |
| dc.subject | Teoria algebraica de nombres | |
| dc.subject | Matrius (Matemàtica) | |
| dc.subject | Treballs de fi de màster | |
| dc.subject | Varietats de Shimura | |
| dc.subject | Quaternions | |
| dc.subject | Algebraic number theory | |
| dc.subject | Matrices | |
| dc.subject | Master's theses | |
| dc.subject | Shimura varieties | |
| dc.subject | Quaternions | |
| dc.title | Families of orders of quaternion algebras over $\mathbb{Q}$ | |
| dc.type | info:eu-repo/semantics/masterThesis |
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