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DC Field | Value | Language |
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dc.contributor.advisor | Travesa i Grau, Artur | - |
dc.contributor.author | Miquel Bleier, Alejandro de | - |
dc.date.accessioned | 2018-03-22T10:25:36Z | - |
dc.date.available | 2018-03-22T10:25:36Z | - |
dc.date.issued | 2017-06-28 | - |
dc.identifier.uri | http://hdl.handle.net/2445/120989 | - |
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 | ca |
dc.description.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, $\mathcla{O}/\mathcal{O'}\cong \mathcla{O'}/\mathcal{O''}\cong \mathcla{O''}/\mathcal{O}\cong\mathbb{Z}/N\mathbb{Z}$. | ca |
dc.format.extent | 29 p. | - |
dc.format.mimetype | application/pdf | - |
dc.language.iso | eng | ca |
dc.rights | cc-by-sa (c) Alejandro de Miquel Bleier, 2017 | - |
dc.rights.uri | http://creativecommons.org/licenses/by-sa/3.0/es/ | - |
dc.source | Màster Oficial - Matemàtica Avançada | - |
dc.subject.classification | Teoria algebraica de nombres | cat |
dc.subject.classification | Matrius (Matemàtica) | cat |
dc.subject.classification | Treballs de fi de màster | cat |
dc.subject.classification | Varietats de Shimura | - |
dc.subject.classification | Quaternions | ca |
dc.subject.other | Algebraic number theory | eng |
dc.subject.other | Matrices | eng |
dc.subject.other | Master's theses | eng |
dc.subject.other | Shimura varieties | en |
dc.subject.other | Quaternions | en |
dc.title | Families of orders of quaternion algebras over $\mathbb{Q}$ | ca |
dc.type | info:eu-repo/semantics/masterThesis | ca |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | ca |
Appears in Collections: | Màster Oficial - Matemàtica Avançada |
Files in This Item:
File | Description | Size | Format | |
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memoria.pdf | Memòria | 273.46 kB | Adobe PDF | View/Open |
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