Torres de extensões abelianas de grau primo ímpar não ramificado

• Ano de defesa: 2015
• Autor(a) principal: Oliveira, Everton Luiz de [UNESP]
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Estadual Paulista (Unesp)
• Palavras-chave em Português: Matemática; Algebra comutativa; Teoria dos números; Teoria dos reticulados
• Link de acesso: http://hdl.handle.net/11449/127722; http://www.athena.biblioteca.unesp.br/exlibris/bd/cathedra/01-09-2015/000844686.pdf

Let L/Q be an abelian extension of odd prime degree p and conductor n, and assume that p is unramified in L/Q. In this work the integral trace form TrL/Q(x2)|OL is given explicitly and some of its properties are derived, in particular the determination of its nonzero minima in certain Z-submodules of the ring of algebraic integers OL. An analysis of the field towers obtained as the composita of number fields of degree p, contained in Q(ζn), is presented. Finally, the integral trace form of the compositum of any two of those p-extensions, when the respective conductors are relatively prime, is described as well