Hecke algebras, deformation rings and singularities
The aim of this work is to cover the main background of Hecke algebras and deformations of Galois Representations, as well as the main results on complete intersection rings used in the most important results on Number Theory (for example, Fermat's Last Theorem). This thesis is thought to intro...
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| Tipo de recurso: | tesis de maestría |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/371988 |
| Acceso en línea: | https://hdl.handle.net/2117/371988 |
| Access Level: | acceso abierto |
| Palabra clave: | Automorphic forms Discontinuous groups Modular Forms Hecke Algebras Galois Representations Deformation Rings of Galois Representations Complete Intersection Rings Formes automòrfiques Grups discontinus Classificació AMS::11 Number theory::11F Discontinuous groups and automorphic forms Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de nombres |
| Sumario: | The aim of this work is to cover the main background of Hecke algebras and deformations of Galois Representations, as well as the main results on complete intersection rings used in the most important results on Number Theory (for example, Fermat's Last Theorem). This thesis is thought to introduce comprehensively (assumed certain knowledge on commutative algebra and modular forms) the basic results on the structure of Hecke algebras and the explicit construction of the Universal Deformation Rings associated to certain Galois representations. |
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