On the number of rational points on curves over finite fields with many automorphisms
Using Weil descent, we give bounds for the number of rational points on two families of curves over finite fields with a large abelian group of automorphisms: Artin–Schreier curves of the form yq−y=f(x) with f∈Fqr[x], on which the additive group Fq acts, and Kummer curves of the form , which have an...
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2013 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/42004 |
| Acceso en línea: | http://hdl.handle.net/11441/42004 https://doi.org/10.1016/j.ffa.2012.11.001 |
| Access Level: | acceso abierto |
| Palabra clave: | Point counting Weil bound ℓ-adic cohomology Weil descent |
| Sumario: | Using Weil descent, we give bounds for the number of rational points on two families of curves over finite fields with a large abelian group of automorphisms: Artin–Schreier curves of the form yq−y=f(x) with f∈Fqr[x], on which the additive group Fq acts, and Kummer curves of the form , which have an action of the multiplicative group . In both cases we can remove a factor from the Weil bound when q is sufficiently large. |
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