Zeta functions of singular curves over finite fields
Let X be a complete, geometrically irreducible, algebraic curve defined over a finite field Fq and let ς (X,t) be its zeta function [Ser1], If X is a singular curve, two other zeta functions exist. The first is the Dirichlet series Z(Ca(X), t) associated to the effective Cartier divisors on X; the s...
| Autor: | |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 1997 |
| País: | Colombia |
| Institución: | Universidad Nacional de Colombia |
| Repositorio: | Repositorio UN |
| Idioma: | español |
| OAI Identifier: | oai:repositorio.unal.edu.co:unal/43675 |
| Acceso en línea: | https://repositorio.unal.edu.co/handle/unal/43675 http://bdigital.unal.edu.co/33773/ |
| Access Level: | acceso abierto |
| Palabra clave: | Zeta functions finite fields singular curves generalized Jacobians compactified Jacobians |
| Sumario: | Let X be a complete, geometrically irreducible, algebraic curve defined over a finite field Fq and let ς (X,t) be its zeta function [Ser1], If X is a singular curve, two other zeta functions exist. The first is the Dirichlet series Z(Ca(X), t) associated to the effective Cartier divisors on X; the second is the Dirichlet series Z(Div(X),t) associated to the effective divisors on X, In this paper we generalize F. K. Schmidt's results on the rationality and functional equation of the zeta function ς(X, t) of a non-singular curve to the functions Z(Ca(X), t) and Z(Div(X), t) by means ofthe singular Riemann-Roch theorem. |
|---|