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...
- 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
- Rights
- openAccess
- License
- Atribución-NoComercial 4.0 Internacional
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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 |
dc.type.driver.spa.fl_str_mv |
info:eu-repo/semantics/masterThesis |
dc.type.version.spa.fl_str_mv |
info:eu-repo/semantics/acceptedVersion |
dc.type.content.spa.fl_str_mv |
Text |
dc.type.redcol.spa.fl_str_mv |
http://purl.org/redcol/resource_type/TM |
status_str |
acceptedVersion |
dc.identifier.uri.none.fl_str_mv |
https://repositorio.unal.edu.co/handle/unal/55782 |
dc.identifier.eprints.spa.fl_str_mv |
http://bdigital.unal.edu.co/51249/ |
url |
https://repositorio.unal.edu.co/handle/unal/55782 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 |
dc.rights.coar.fl_str_mv |
http://purl.org/coar/access_right/c_abf2 |
dc.rights.license.spa.fl_str_mv |
Atribución-NoComercial 4.0 Internacional |
dc.rights.uri.spa.fl_str_mv |
http://creativecommons.org/licenses/by-nc/4.0/ |
dc.rights.accessrights.spa.fl_str_mv |
info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
Atribución-NoComercial 4.0 Internacional Derechos reservados - Universidad Nacional de Colombia http://creativecommons.org/licenses/by-nc/4.0/ http://purl.org/coar/access_right/c_abf2 |
eu_rights_str_mv |
openAccess |
dc.format.mimetype.spa.fl_str_mv |
application/pdf |
institution |
Universidad Nacional de Colombia |
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