The finitistic dimension conjecture

Detalhes bibliográficos
Autor(a) principal: Júlio César Magalhães Marques
Data de Publicação: 2019
Tipo de documento: Dissertação
Idioma: eng
Título da fonte: Repositório Institucional da UFMG
Texto Completo: http://hdl.handle.net/1843/36254
Resumo: We study two conditions under which the finitistic dimension conjecture holds. First, we study an article by K. Igusa and G. Todorov, which gives a simple condition that implies the finiteness of the little finitistic dimension for Artin algebras. We present their short proof of the finitistic dimension conjecture for radical cubed zero algebras and for algebras with representation dimension smaller than or equal to three. Secondly, following a recent article by J. Rickard, we considered the question of whether the injective modules generate the unbounded derived category of a ring as a triangulated category with arbitrary coproducts. We present Rickard's proof that if injectives generate for such algebra, then the big finitistic dimension conjecture holds for that algebra.
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spelling John William MacQuarriehttp://lattes.cnpq.br/7878226069423105Flávio Ulhoa CoelhoViktor Bekkerthttp://lattes.cnpq.br/9052028483281224Júlio César Magalhães Marques2021-06-02T15:49:58Z2021-06-02T15:49:58Z2019-08-23http://hdl.handle.net/1843/36254We study two conditions under which the finitistic dimension conjecture holds. First, we study an article by K. Igusa and G. Todorov, which gives a simple condition that implies the finiteness of the little finitistic dimension for Artin algebras. We present their short proof of the finitistic dimension conjecture for radical cubed zero algebras and for algebras with representation dimension smaller than or equal to three. Secondly, following a recent article by J. Rickard, we considered the question of whether the injective modules generate the unbounded derived category of a ring as a triangulated category with arbitrary coproducts. We present Rickard's proof that if injectives generate for such algebra, then the big finitistic dimension conjecture holds for that algebra.Estudamos duas condições sob as quais a conjectura da dimensão finitística é válida. Primeiro, estudamos um artigo de K. Igusa e G. Todorov, que fornece uma condição simples que implica a finitude da pequena dimensão finitística para álgebras de Artin. Apresentamos sua prova curta da conjectura da dimensão finitística para álgebras com radicais ao cubo igual a zero e para álgebras com dimensão de representação menor ou igual a três. Em segundo lugar, seguindo um artigo recente de J. Rickard, consideramos a questão de saber se os módulos injetivos geram a categoria derivada ilimitada de um anel como uma categoria triangulada com coprodutos arbitrários. Apresentamos a prova de Rickard de que, se os injetivos geram para essa álgebra, então a grande conjectura de dimensão finitística se aplica a essa álgebra.CNPq - Conselho Nacional de Desenvolvimento Científico e TecnológicoengUniversidade Federal de Minas GeraisPrograma de Pós-Graduação em MatemáticaUFMGBrasilICX - DEPARTAMENTO DE MATEMÁTICAMatemática– Teses.Artin algebras– Teses.Dimensão de Representação– TesesFinitistic dimension conjectureDerived categoryArtin algebraInjectives generateRepresentation dimension.The finitistic dimension conjectureA conjectura da dimensão finitistainfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFMGinstname:Universidade Federal de Minas Gerais (UFMG)instacron:UFMGORIGINALThe Finitistic Dimension Conjecture - Júlio Marques.pdfThe Finitistic Dimension Conjecture - Júlio Marques.pdfapplication/pdf1232920https://repositorio.ufmg.br/bitstream/1843/36254/5/The%20Finitistic%20Dimension%20Conjecture%20-%20J%c3%balio%20Marques.pdf100ae26a6e1b5fa2bd51996962082d54MD55LICENSElicense.txtlicense.txttext/plain; charset=utf-82119https://repositorio.ufmg.br/bitstream/1843/36254/6/license.txt34badce4be7e31e3adb4575ae96af679MD561843/362542021-06-02 12:49:58.151oai:repositorio.ufmg.br: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Repositório de PublicaçõesPUBhttps://repositorio.ufmg.br/oaiopendoar:2021-06-02T15:49:58Repositório Institucional da UFMG - Universidade Federal de Minas Gerais (UFMG)false
dc.title.pt_BR.fl_str_mv The finitistic dimension conjecture
dc.title.alternative.pt_BR.fl_str_mv A conjectura da dimensão finitista
title The finitistic dimension conjecture
spellingShingle The finitistic dimension conjecture
Júlio César Magalhães Marques
Finitistic dimension conjecture
Derived category
Artin algebra
Injectives generate
Representation dimension.
Matemática– Teses.
Artin algebras– Teses.
Dimensão de Representação– Teses
title_short The finitistic dimension conjecture
title_full The finitistic dimension conjecture
title_fullStr The finitistic dimension conjecture
title_full_unstemmed The finitistic dimension conjecture
title_sort The finitistic dimension conjecture
author Júlio César Magalhães Marques
author_facet Júlio César Magalhães Marques
author_role author
dc.contributor.advisor1.fl_str_mv John William MacQuarrie
dc.contributor.advisor1Lattes.fl_str_mv http://lattes.cnpq.br/7878226069423105
dc.contributor.referee1.fl_str_mv Flávio Ulhoa Coelho
dc.contributor.referee2.fl_str_mv Viktor Bekkert
dc.contributor.authorLattes.fl_str_mv http://lattes.cnpq.br/9052028483281224
dc.contributor.author.fl_str_mv Júlio César Magalhães Marques
contributor_str_mv John William MacQuarrie
Flávio Ulhoa Coelho
Viktor Bekkert
dc.subject.por.fl_str_mv Finitistic dimension conjecture
Derived category
Artin algebra
Injectives generate
Representation dimension.
topic Finitistic dimension conjecture
Derived category
Artin algebra
Injectives generate
Representation dimension.
Matemática– Teses.
Artin algebras– Teses.
Dimensão de Representação– Teses
dc.subject.other.pt_BR.fl_str_mv Matemática– Teses.
Artin algebras– Teses.
Dimensão de Representação– Teses
description We study two conditions under which the finitistic dimension conjecture holds. First, we study an article by K. Igusa and G. Todorov, which gives a simple condition that implies the finiteness of the little finitistic dimension for Artin algebras. We present their short proof of the finitistic dimension conjecture for radical cubed zero algebras and for algebras with representation dimension smaller than or equal to three. Secondly, following a recent article by J. Rickard, we considered the question of whether the injective modules generate the unbounded derived category of a ring as a triangulated category with arbitrary coproducts. We present Rickard's proof that if injectives generate for such algebra, then the big finitistic dimension conjecture holds for that algebra.
publishDate 2019
dc.date.issued.fl_str_mv 2019-08-23
dc.date.accessioned.fl_str_mv 2021-06-02T15:49:58Z
dc.date.available.fl_str_mv 2021-06-02T15:49:58Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/masterThesis
format masterThesis
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/1843/36254
url http://hdl.handle.net/1843/36254
dc.language.iso.fl_str_mv eng
language eng
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Universidade Federal de Minas Gerais
dc.publisher.program.fl_str_mv Programa de Pós-Graduação em Matemática
dc.publisher.initials.fl_str_mv UFMG
dc.publisher.country.fl_str_mv Brasil
dc.publisher.department.fl_str_mv ICX - DEPARTAMENTO DE MATEMÁTICA
publisher.none.fl_str_mv Universidade Federal de Minas Gerais
dc.source.none.fl_str_mv reponame:Repositório Institucional da UFMG
instname:Universidade Federal de Minas Gerais (UFMG)
instacron:UFMG
instname_str Universidade Federal de Minas Gerais (UFMG)
instacron_str UFMG
institution UFMG
reponame_str Repositório Institucional da UFMG
collection Repositório Institucional da UFMG
bitstream.url.fl_str_mv https://repositorio.ufmg.br/bitstream/1843/36254/5/The%20Finitistic%20Dimension%20Conjecture%20-%20J%c3%balio%20Marques.pdf
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