Homologia de André-Quillen para Álgebras Comutativas

• Ano de defesa: 2017
• Autor(a) principal: Silva, Ricardo Bruno Alves da
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal da Paraíba; Brasil; Matemática; Programa de Pós-Graduação em Matemática; UFPB
• Palavras-chave em Português: Diferenciais de Kahler; álgebras; módulos simpliciais; homologia de André-Quillen; Simplied modules; Homology of André-Quillen; Dierentials of Kahler; algebras; CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: https://repositorio.ufpb.br/jspui/handle/tede/9831

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.