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

Nazar Arakelian; Herivelto Borges

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arXiv · 1409.8549

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

Nazar Arakelian·Herivelto Borges

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Abstract

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.

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Nazar Arakelian, Herivelto Borges. 2014-09-30. Frobenius nonclassicality with respect to linear systems of curves of arbitrary degree. https://arxiv.org/abs/1409.8549

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