Teorema de Riemann-Roch, morfismos de Frobenius e a hipótese de Riemann

• Ano de defesa: 2014
• Autor(a) principal: Silva Junior, Roberto Carlos Alvarenga da [UNESP]
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Estadual Paulista (Unesp)
• Palavras-chave em Português: Matemática; Geometria algebrica; Geometria algebrica aritmetica; Riemann-Roch, Teoremas de; Hipótese de Riemann; Funções Zeta; Geometry, Algebraic
• Link de acesso: http://hdl.handle.net/11449/122107

The aim of this work is to estimate a bound for the number of rational points of a curve. Observing the various similarities between the ring of integers and the ring of polynomials in one variable, we use tools from number theory to solve a problem of algebraic geometry. From this merger is born one of the noblest areas of mathematics: arithmetic geometry. Making use of the famous Riemann-Roch's theorem and tools of number theory we demonstrate the Riemann hypothesis for the zeta-function of a nonsingular curve and which consequence this hypothesis has to count rational points on a curve