Frobenius nonclassicality with respect to linear systems of curves of arbitrary degree

• Autorzy: Nazar Arakelian , Herivelto Borges
• Języki publikacji: EN

Abstrakty

EN

For each integer s ≥ 1, we present a family of curves that are $𝔽_q$-Frobenius nonclassical with respect to the linear system of plane curves of degree s. In the case s=2, we give necessary and sufficient conditions for such curves to be $𝔽_q$-Frobenius nonclassical with respect to the linear system of conics. In the $𝔽_q$-Frobenius nonclassical cases, we determine the exact number of $𝔽_q$-rational points. In the remaining cases, an upper bound for the number of $𝔽_q$-rational points will follow from Stöhr-Voloch theory.

Kategorie tematyczne

• 11G20: Curves over finite and local fields
• 14Hxx: Curves
• 14H05: Algebraic functions; function fields

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2015
• Tom: 167
• Numer: 1
• Strony: 43-66

Daty

wydano

2015

Twórcy

autor

Nazar Arakelian

• Instituto de Matemática, Estatística, e Computaçõ Científica, Universidade Estadual de Campinas, Rua Sérgio Buarque de Holanda, 651, CEP 13083-859, Campinas SP, Brazil

autor

Herivelto Borges

• Instituto de Ciências Matemáticas, e de Computação, Universidade de São Paulo, Avenida Trabalhador São-carlense, 400, CEP 13566-590, São Carlos SP, Brazil

Identyfikatory

DOI

10.4064/aa167-1-3