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

• Ano de defesa: 2020
• Autor(a) principal: Júnior, Cirilo Gonçalves
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: 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
• Link de acesso: https://www.teses.usp.br/teses/disponiveis/55/55135/tde-10062020-134739/

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.