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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

Álgebras simétrica e de Rees do módulo de diferenciais de Kähler

Sousa, Fraciélia Limeira de 16 July 2015 (has links)
Submitted by Maike Costa (maiksebas@gmail.com) on 2016-03-31T13:40:38Z No. of bitstreams: 1 arquivo total.pdf: 1581712 bytes, checksum: 55cfc2e330d11ed8545538014daa3873 (MD5) / Made available in DSpace on 2016-03-31T13:40:38Z (GMT). No. of bitstreams: 1 arquivo total.pdf: 1581712 bytes, checksum: 55cfc2e330d11ed8545538014daa3873 (MD5) Previous issue date: 2015-07-16 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this dissertation, we initially present an overview about the symmetric and the Rees algebras in the wide context of modules, and we consider particularly the special situation in which the given module possesses a linear presentation. In the sequel, the main goal is the study of such blowup algebras in the case where the module is the celebrated module of K ahler di erentials, the focus being given on the investigation of an interesting version of the long-standing Berger's Conjecture for the symmetric algebra, as well as on the study of fundamental properties such as: integrality, Cohen- Macaulayness and normality; these properties are also investigated in a special way in the case of the Rees algebra (of the di erential module), highlighting the connection to the so-called Fitting conditions. / Nesta disserta c~ao, inicialmente apresentamos no c~oes gerais sobre a algebra sim etrica e a algebra de Rees no contexto amplo de m odulos, e consideramos particularmente a situa c~ao especial na qual o dado m odulo possui apresenta c~ao linear. Na sequ^encia, o principal objetivo e o estudo de tais algebras de blowup no caso em que o m odulo e o celebrado m odulo de diferenciais de K ahler, tendo como foco a investiga c~ao de uma interessante vers~ao da persistente Conjectura de Berger para a algebra sim etrica, bem como o estudo de propriedades fundamentais como: integridade, Cohen-Macaulicidade e normalidade; tais propriedades s~ao tamb em investigadas de forma especial no caso da algebra de Rees (do m odulo de diferenciais), evidenciando inclusive a conex~ao com as chamadas condi c~oes de Fitting.
2

Homologia de André-Quillen para Álgebras Comutativas

Silva, Ricardo Bruno Alves da 27 April 2017 (has links)
Submitted by Leonardo Cavalcante (leo.ocavalcante@gmail.com) on 2018-05-02T14:09:22Z No. of bitstreams: 1 Arquivototal.pdf: 978771 bytes, checksum: bf0c05c8da5e986a77b6215a2235ab5e (MD5) / Made available in DSpace on 2018-05-02T14:09:22Z (GMT). No. of bitstreams: 1 Arquivototal.pdf: 978771 bytes, checksum: bf0c05c8da5e986a77b6215a2235ab5e (MD5) Previous issue date: 2017-04-27 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / At the end of the 60s, Andr e and Quillen introduced a cohomology theory for commutative algebras, which today is called Andr e-Quillen's cohomology. In this work, we will study K ahler di erential functor, which is here seen as a derived functor (in a nonabelian context), which connects the categories: simpli ed R-algebras and simpli ed R-modules. In the rst, through simplicial resolutions, we will notice that they characterize certain objects and diagrams of this model category, which in turn, are preserved by K ahler di erential functor. In addition, we will approach the complex cotangent of a R-algebra, and through it, de ne the homology and cohomology of Andr e-Quilen, and of course, expose some properties of these. / No nal da década de 60, André e Quillen introduziram uma teoria de cohomologia para álgebras comutativas, que hoje recebe o nome de cohomologia de André-Quillen. Neste trabalho, estudaremos o funtor de diferenciais de K ahler, que aqui é visto como funtor derivado (em um contexto não abeliano), que conecta as categorias: R-álgebras simpliciais e R-m odulos simpliciais. Na primeira, atrav es das resolu c~oes simpliciais, notaremos que estas caracterizam certos objetos e diagramas desta categoria modelo, que por sua vez, s~ao preservados pelo funtor de diferenciais de K ahler. Al em disso, abordaremos o complexo cotangente de uma R- algebra, e atrav es dele, de nir a homologia e cohomologia de André-Quillen, e naturalmente, expor algumas propriedades destas.

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