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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Detalles Bibliográficos
Autor: Guillán Rial, Javier
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
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spelling Hecke algebras, deformation rings and singularitiesGuillán Rial, JavierAutomorphic formsDiscontinuous groupsModular FormsHecke AlgebrasGalois RepresentationsDeformation Rings of Galois RepresentationsComplete Intersection RingsFormes automòrfiquesGrups discontinusClassificació AMS::11 Number theory::11F Discontinuous groups and automorphic formsÀrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de nombresThe 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.Universitat Politècnica de CatalunyaRotger Cerdà, Víctor20222022-07-0120222022-08-30master thesishttp://purl.org/coar/resource_type/c_bdccNAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/masterThesisapplication/pdfhttps://hdl.handle.net/2117/371988reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2http://creativecommons.org/licenses/by-nc-sa/3.0/es/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/3719882026-05-27T15:37:01Z
dc.title.none.fl_str_mv Hecke algebras, deformation rings and singularities
title Hecke algebras, deformation rings and singularities
spellingShingle Hecke algebras, deformation rings and singularities
Guillán Rial, Javier
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
title_short Hecke algebras, deformation rings and singularities
title_full Hecke algebras, deformation rings and singularities
title_fullStr Hecke algebras, deformation rings and singularities
title_full_unstemmed Hecke algebras, deformation rings and singularities
title_sort Hecke algebras, deformation rings and singularities
dc.creator.none.fl_str_mv Guillán Rial, Javier
author Guillán Rial, Javier
author_facet Guillán Rial, Javier
author_role author
dc.contributor.none.fl_str_mv Rotger Cerdà, Víctor
dc.subject.none.fl_str_mv 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
topic 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
description 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.
publishDate 2022
dc.date.none.fl_str_mv 2022
2022-07-01
2022
2022-08-30
dc.type.none.fl_str_mv master thesis
http://purl.org/coar/resource_type/c_bdcc
NA
http://purl.org/coar/version/c_be7fb7dd8ff6fe43
dc.type.openaire.fl_str_mv info:eu-repo/semantics/masterThesis
format masterThesis
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/371988
url https://hdl.handle.net/2117/371988
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2

http://creativecommons.org/licenses/by-nc-sa/3.0/es/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2

http://creativecommons.org/licenses/by-nc-sa/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Universitat Politècnica de Catalunya
publisher.none.fl_str_mv Universitat Politècnica de Catalunya
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300724

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