Grothendieck topologies, fibered categories and descent theory: an introduction to the stack theory

The notion of stack grew out of attempts to parameterize geometric objects varying in families. Such families are classically know as Moduli and their understanding is a central theme in Algebraic Geometry. The formalism of stacks was introduced by A. Grothendieck and M. Artin as the natural context...

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Autores:
Vivares Parra, Carlos Eduardo
Tipo de recurso:
Fecha de publicación:
2015
Institución:
Universidad Nacional de Colombia
Repositorio:
Universidad Nacional de Colombia
Idioma:
spa
OAI Identifier:
oai:repositorio.unal.edu.co:unal/55782
Acceso en línea:
https://repositorio.unal.edu.co/handle/unal/55782
http://bdigital.unal.edu.co/51249/
Palabra clave:
51 Matemáticas / Mathematics
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openAccess
License
Atribución-NoComercial 4.0 Internacional
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spelling Atribución-NoComercial 4.0 InternacionalDerechos reservados - Universidad Nacional de Colombiahttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Vélez Caicedo, Juan DiegoVivares Parra, Carlos Eduardo47c1811a-cf67-44d9-9734-629de0d99c453002019-07-02T11:28:15Z2019-07-02T11:28:15Z2015https://repositorio.unal.edu.co/handle/unal/55782http://bdigital.unal.edu.co/51249/The notion of stack grew out of attempts to parameterize geometric objects varying in families. Such families are classically know as Moduli and their understanding is a central theme in Algebraic Geometry. The formalism of stacks was introduced by A. Grothendieck and M. Artin as the natural context in which moduli problems of objects with symmetries can be tackled. The usual spaces used in geometry– Manifolds, Varieties, Schemes– are inadequate for the parametrization of geometry objects that are self similar. Instead one needs a procedure that will not only encode the way things vary in families but will also remembers the intrinsic symmetries of each object in the family. As an example, let us consider two families of ellipses parametrized by a circle: The left-hand family is trivial, all the ellipses in this one are positioned in exactly the same way. The ellipses in the right-hand family are all the same but they are rotated in their planes. Families of this kind are called isotrivial. The usual parameter spaces do not capture the distinction between trivial and isotrivial families.Maestríaapplication/pdfspaUniversidad Nacional de Colombia Sede Medellín Facultad de Ciencias Escuela de MatemáticasEscuela de MatemáticasVivares Parra, Carlos Eduardo (2015) Grothendieck topologies, fibered categories and descent theory: an introduction to the stack theory. Maestría thesis, Universidad Nacional de Colombia - Sede Medellín.51 Matemáticas / MathematicsGrothendieck topologies, fibered categories and descent theory: an introduction to the stack theoryTrabajo de grado - Maestríainfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/acceptedVersionTexthttp://purl.org/redcol/resource_type/TMORIGINAL71194742.2015.pdfTesis de Maestría en Ciencias - Matemáticasapplication/pdf680161https://repositorio.unal.edu.co/bitstream/unal/55782/1/71194742.2015.pdf702cc34b15ac8b5686435dcf27356f16MD51THUMBNAIL71194742.2015.pdf.jpg71194742.2015.pdf.jpgGenerated Thumbnailimage/jpeg3785https://repositorio.unal.edu.co/bitstream/unal/55782/2/71194742.2015.pdf.jpgf3b57b4911361010010511701819bd42MD52unal/55782oai:repositorio.unal.edu.co:unal/557822023-04-18 11:25:10.373Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.co
dc.title.spa.fl_str_mv Grothendieck topologies, fibered categories and descent theory: an introduction to the stack theory
title Grothendieck topologies, fibered categories and descent theory: an introduction to the stack theory
spellingShingle Grothendieck topologies, fibered categories and descent theory: an introduction to the stack theory
51 Matemáticas / Mathematics
title_short Grothendieck topologies, fibered categories and descent theory: an introduction to the stack theory
title_full Grothendieck topologies, fibered categories and descent theory: an introduction to the stack theory
title_fullStr Grothendieck topologies, fibered categories and descent theory: an introduction to the stack theory
title_full_unstemmed Grothendieck topologies, fibered categories and descent theory: an introduction to the stack theory
title_sort Grothendieck topologies, fibered categories and descent theory: an introduction to the stack theory
dc.creator.fl_str_mv Vivares Parra, Carlos Eduardo
dc.contributor.author.spa.fl_str_mv Vivares Parra, Carlos Eduardo
dc.contributor.spa.fl_str_mv Vélez Caicedo, Juan Diego
dc.subject.ddc.spa.fl_str_mv 51 Matemáticas / Mathematics
topic 51 Matemáticas / Mathematics
description The notion of stack grew out of attempts to parameterize geometric objects varying in families. Such families are classically know as Moduli and their understanding is a central theme in Algebraic Geometry. The formalism of stacks was introduced by A. Grothendieck and M. Artin as the natural context in which moduli problems of objects with symmetries can be tackled. The usual spaces used in geometry– Manifolds, Varieties, Schemes– are inadequate for the parametrization of geometry objects that are self similar. Instead one needs a procedure that will not only encode the way things vary in families but will also remembers the intrinsic symmetries of each object in the family. As an example, let us consider two families of ellipses parametrized by a circle: The left-hand family is trivial, all the ellipses in this one are positioned in exactly the same way. The ellipses in the right-hand family are all the same but they are rotated in their planes. Families of this kind are called isotrivial. The usual parameter spaces do not capture the distinction between trivial and isotrivial families.
publishDate 2015
dc.date.issued.spa.fl_str_mv 2015
dc.date.accessioned.spa.fl_str_mv 2019-07-02T11:28:15Z
dc.date.available.spa.fl_str_mv 2019-07-02T11:28:15Z
dc.type.spa.fl_str_mv Trabajo de grado - Maestría
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http://bdigital.unal.edu.co/51249/
dc.language.iso.spa.fl_str_mv spa
language spa
dc.relation.ispartof.spa.fl_str_mv Universidad Nacional de Colombia Sede Medellín Facultad de Ciencias Escuela de Matemáticas
Escuela de Matemáticas
dc.relation.references.spa.fl_str_mv Vivares Parra, Carlos Eduardo (2015) Grothendieck topologies, fibered categories and descent theory: an introduction to the stack theory. Maestría thesis, Universidad Nacional de Colombia - Sede Medellín.
dc.rights.spa.fl_str_mv Derechos reservados - Universidad Nacional de Colombia
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rights_invalid_str_mv Atribución-NoComercial 4.0 Internacional
Derechos reservados - Universidad Nacional de Colombia
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eu_rights_str_mv openAccess
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