On Fq3 -Frobenius nonclassical curvces of type Yq2+q+1 = f (X) and the Hasse-Witt invariant for a class of Kummer extension

Inserted in the context of algebraic curves defined over finite fields, this work presents several results in two different topics. First, it gives a complete characterization of the Fq3 -Frobenius nonclassical curves of type Yq2+q+1 = f (X), and it provides an explicit computation of the following...

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Detalles Bibliográficos
Autor: Gonçalves Júnior, Cirilo
Tipo de recurso: tesis doctoral
Estado:Versión publicada
Fecha de publicación:2020
País:Brasil
Institución:Universidade de São Paulo (USP)
Repositorio:Biblioteca Digital de Teses e Dissertações da USP
Idioma:inglés
OAI Identifier:oai:teses.usp.br:tde-10062020-134739
Acceso en línea:https://www.teses.usp.br/teses/disponiveis/55/55135/tde-10062020-134739/
Access Level:acceso abierto
Palabra clave:α-number
Automorphism group
Curvas Frobenius não-classicas
Curvas hiperelípticas
Frobenius nonclassical curves
Grupo de automorfismo
Hasse-Witt invariant
Hyperelliptic curves
Invariante de Hasse-Witt
Descripción
Sumario:Inserted in the context of algebraic curves defined over finite fields, this work presents several results in two different topics. First, it gives a complete characterization of the Fq3 -Frobenius nonclassical curves of type Yq2+q+1 = f (X), and it provides an explicit computation of the following birational invariants: genus, automorphism group, Hasse-Witt invariant and a-number. The number of Fq3 -rational points is computed as well. Second, this work provides an extensive study of the Hasse-Witt invariant of the curves Ym +Xn +1 = 0 and Ym +Xn +X = 0. A combinatorial formula for this invariant is presented in the general case, and explicit closed formulas are provided for special values of m and n.