Cohomology of quasi-coherent sheaves over projective schemes

Detalhes bibliográficos
Autor(a) principal: Alvarez, Daniel Alberto Aguilar
Data de Publicação: 2021
Tipo de documento: Dissertação
Idioma: eng
Título da fonte: Biblioteca Digital de Teses e Dissertações da USP
Texto Completo: https://www.teses.usp.br/teses/disponiveis/55/55135/tde-11082021-113531/
Resumo: The objective of this work is to present the reader with the study of some mathematical tools used in current problems of algebraic geometry, assuming only some knowledge in algebra and topology. We treat basic concepts and results in the theory of sheaves and schemes that we later use to understand the correspondence between local cohomology and sheaf cohomology of quasi-coherent sheaves over projective schemes. Then, with this background we are able to state some open problems that are related to the Hilbert polynomial and to the Castelonuovo-Mumford regularity of a coherent sheaf.
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spelling Cohomology of quasi-coherent sheaves over projective schemesCohomologia de feixes quasi-coherentes sobre esquemas projetivosCohomologia de feixesCohomologia localEsquema projetivoFeixe quasi-coherenteLocal cohomologyProjective schemeQuasi- coherent sheafSheaf cohomologyThe objective of this work is to present the reader with the study of some mathematical tools used in current problems of algebraic geometry, assuming only some knowledge in algebra and topology. We treat basic concepts and results in the theory of sheaves and schemes that we later use to understand the correspondence between local cohomology and sheaf cohomology of quasi-coherent sheaves over projective schemes. Then, with this background we are able to state some open problems that are related to the Hilbert polynomial and to the Castelonuovo-Mumford regularity of a coherent sheaf.O objetivo deste trabalho é apresentar ao leitor o estudo de algumas ferramentas matemáticas utilizadas nos problemas atuais da geometria algébrica, pressupondo apenas alguns conhecimentos em álgebra e topologia. Expõe conceitos e resultados básicos na teoria de feixes e esquemas, que logo são usados para entender a correspondência que existe entre a cohomologia local e a cohomologia de feixes, no caso de feixes quasi-coherentes sobre esquemas projetivos. Finalmente enunciamos alguns problemas em aberto relacionados com o polinômio de Hilbert e a regularidade de Castelonuovo-Mumford de um feixe coherente.Biblioteca Digitais de Teses e Dissertações da USPPérez, Victor Hugo JorgeAlvarez, Daniel Alberto Aguilar2021-05-28info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisapplication/pdfhttps://www.teses.usp.br/teses/disponiveis/55/55135/tde-11082021-113531/reponame:Biblioteca Digital de Teses e Dissertações da USPinstname:Universidade de São Paulo (USP)instacron:USPLiberar o conteúdo para acesso público.info:eu-repo/semantics/openAccesseng2021-08-11T22:13:02Zoai:teses.usp.br:tde-11082021-113531Biblioteca Digital de Teses e Dissertaçõeshttp://www.teses.usp.br/PUBhttp://www.teses.usp.br/cgi-bin/mtd2br.plvirginia@if.usp.br|| atendimento@aguia.usp.br||virginia@if.usp.bropendoar:27212021-08-11T22:13:02Biblioteca Digital de Teses e Dissertações da USP - Universidade de São Paulo (USP)false
dc.title.none.fl_str_mv Cohomology of quasi-coherent sheaves over projective schemes
Cohomologia de feixes quasi-coherentes sobre esquemas projetivos
title Cohomology of quasi-coherent sheaves over projective schemes
spellingShingle Cohomology of quasi-coherent sheaves over projective schemes
Alvarez, Daniel Alberto Aguilar
Cohomologia de feixes
Cohomologia local
Esquema projetivo
Feixe quasi-coherente
Local cohomology
Projective scheme
Quasi- coherent sheaf
Sheaf cohomology
title_short Cohomology of quasi-coherent sheaves over projective schemes
title_full Cohomology of quasi-coherent sheaves over projective schemes
title_fullStr Cohomology of quasi-coherent sheaves over projective schemes
title_full_unstemmed Cohomology of quasi-coherent sheaves over projective schemes
title_sort Cohomology of quasi-coherent sheaves over projective schemes
author Alvarez, Daniel Alberto Aguilar
author_facet Alvarez, Daniel Alberto Aguilar
author_role author
dc.contributor.none.fl_str_mv Pérez, Victor Hugo Jorge
dc.contributor.author.fl_str_mv Alvarez, Daniel Alberto Aguilar
dc.subject.por.fl_str_mv Cohomologia de feixes
Cohomologia local
Esquema projetivo
Feixe quasi-coherente
Local cohomology
Projective scheme
Quasi- coherent sheaf
Sheaf cohomology
topic Cohomologia de feixes
Cohomologia local
Esquema projetivo
Feixe quasi-coherente
Local cohomology
Projective scheme
Quasi- coherent sheaf
Sheaf cohomology
description The objective of this work is to present the reader with the study of some mathematical tools used in current problems of algebraic geometry, assuming only some knowledge in algebra and topology. We treat basic concepts and results in the theory of sheaves and schemes that we later use to understand the correspondence between local cohomology and sheaf cohomology of quasi-coherent sheaves over projective schemes. Then, with this background we are able to state some open problems that are related to the Hilbert polynomial and to the Castelonuovo-Mumford regularity of a coherent sheaf.
publishDate 2021
dc.date.none.fl_str_mv 2021-05-28
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 https://www.teses.usp.br/teses/disponiveis/55/55135/tde-11082021-113531/
url https://www.teses.usp.br/teses/disponiveis/55/55135/tde-11082021-113531/
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv
dc.rights.driver.fl_str_mv Liberar o conteúdo para acesso público.
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Liberar o conteúdo para acesso público.
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.coverage.none.fl_str_mv
dc.publisher.none.fl_str_mv Biblioteca Digitais de Teses e Dissertações da USP
publisher.none.fl_str_mv Biblioteca Digitais de Teses e Dissertações da USP
dc.source.none.fl_str_mv
reponame:Biblioteca Digital de Teses e Dissertações da USP
instname:Universidade de São Paulo (USP)
instacron:USP
instname_str Universidade de São Paulo (USP)
instacron_str USP
institution USP
reponame_str Biblioteca Digital de Teses e Dissertações da USP
collection Biblioteca Digital de Teses e Dissertações da USP
repository.name.fl_str_mv Biblioteca Digital de Teses e Dissertações da USP - Universidade de São Paulo (USP)
repository.mail.fl_str_mv virginia@if.usp.br|| atendimento@aguia.usp.br||virginia@if.usp.br
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