An upper bound for the minimum genus of a curve without points of small degree
Volume 160 / 2013
Acta Arithmetica 160 (2013), 115-128
MSC: Primary 11G05; Secondary 11R37.
DOI: 10.4064/aa160-2-2
Abstract
We prove that for any prime $p$ there is a constant $C_p>0$ such that for any $n>0$ and for any $p$-power $q$ there is a smooth, projective, absolutely irreducible curve over $\mathbb {F}_q$ of genus $g\leq C_p q^n$ without points of degree smaller than $n$.
