Frobenius nonclassicality with respect to
linear systems of curves of arbitrary degree
Acta Arithmetica, Tome 167 (2015) no. 1, pp. 43-66
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
For each integer $s \geq 1$, we present a family of curves that are $\mathbb {F}_q$-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 $\mathbb {F}_q$-Frobenius nonclassical with respect to the linear system of conics. In the $\mathbb {F}_q$-Frobenius nonclassical cases, we determine the exact number of $\mathbb {F}_q$-rational points. In the remaining cases, an upper bound for the number of $\mathbb {F}_q$-rational points will follow from Stöhr–Voloch theory.
Keywords:
each integer geq present family curves mathbb q frobenius nonclassical respect linear system plane curves degree necessary sufficient conditions curves mathbb q frobenius nonclassical respect linear system conics mathbb q frobenius nonclassical cases determine exact number mathbb q rational points remaining cases upper bound number mathbb q rational points follow voloch theory
Affiliations des auteurs :
Nazar Arakelian 1 ; Herivelto Borges 2
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author = {Nazar Arakelian and Herivelto Borges},
title = {Frobenius nonclassicality with respect to
linear systems of curves of arbitrary degree},
journal = {Acta Arithmetica},
pages = {43--66},
publisher = {mathdoc},
volume = {167},
number = {1},
year = {2015},
doi = {10.4064/aa167-1-3},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/aa167-1-3/}
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Nazar Arakelian; Herivelto Borges. Frobenius nonclassicality with respect to linear systems of curves of arbitrary degree. Acta Arithmetica, Tome 167 (2015) no. 1, pp. 43-66. doi: 10.4064/aa167-1-3
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