| 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 |
|