For each integer s ≥ 1, we present a family of curves that are -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 -Frobenius nonclassical with respect to the linear system of conics. In the -Frobenius nonclassical cases, we determine the exact number of -rational points. In the remaining cases, an upper bound for the number of -rational points will follow from Stöhr-Voloch theory.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa167-1-3,
author = {Nazar Arakelian and Herivelto Borges},
title = {Frobenius nonclassicality with respect to linear systems of curves of arbitrary degree},
journal = {Acta Arithmetica},
volume = {168},
year = {2015},
pages = {43-66},
zbl = {06390254},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa167-1-3}
}
Nazar Arakelian; Herivelto Borges. Frobenius nonclassicality with respect to linear systems of curves of arbitrary degree. Acta Arithmetica, Tome 168 (2015) pp. 43-66. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa167-1-3/