An upper bound for the genus of a curve without points of small degree

Details An upper bound for the genus of a curve without points of small degree An upper bound for the genus of a curve without points of small degree

2012-03-05

arxiv.org/abs/1203.0945v1

Mathematics

Number Theory

This is part of a Phd thesis at Universit\`a 'Sapienza' of Rome

Scientific paper

In this paper I 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 $n$.

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