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

Nazar Arakelian, and Herivelto Borges. "Frobenius nonclassicality with respect to linear systems of curves of arbitrary degree." Acta Arithmetica 167.1 (2015): 43-66. <http://eudml.org/doc/279025>.

@article{NazarArakelian2015,
abstract = {For each integer s ≥ 1, we present a family of curves that are $_q$-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 $_q$-Frobenius nonclassical with respect to the linear system of conics. In the $_q$-Frobenius nonclassical cases, we determine the exact number of $_q$-rational points. In the remaining cases, an upper bound for the number of $_q$-rational points will follow from Stöhr-Voloch theory.},
author = {Nazar Arakelian, Herivelto Borges},
journal = {Acta Arithmetica},
keywords = {Stöhr-Voloch theory; Frobenius nonclassical curves; finite fields},
language = {eng},
number = {1},
pages = {43-66},
title = {Frobenius nonclassicality with respect to linear systems of curves of arbitrary degree},
url = {http://eudml.org/doc/279025},
volume = {167},
year = {2015},
}

TY - JOUR
AU - Nazar Arakelian
AU - Herivelto Borges
TI - Frobenius nonclassicality with respect to linear systems of curves of arbitrary degree
JO - Acta Arithmetica
PY - 2015
VL - 167
IS - 1
SP - 43
EP - 66
AB - For each integer s ≥ 1, we present a family of curves that are $_q$-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 $_q$-Frobenius nonclassical with respect to the linear system of conics. In the $_q$-Frobenius nonclassical cases, we determine the exact number of $_q$-rational points. In the remaining cases, an upper bound for the number of $_q$-rational points will follow from Stöhr-Voloch theory.
LA - eng
KW - Stöhr-Voloch theory; Frobenius nonclassical curves; finite fields
UR - http://eudml.org/doc/279025
ER -