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

Volume 160 / 2013

Claudio Stirpe Acta Arithmetica 160 (2013), 115-128 MSC: Primary 11G05; Secondary 11R37. DOI: 10.4064/aa160-2-2


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 $n$.


  • Claudio StirpeDipartimento di Matematica
    Università di Roma `Sapienza'
    Via Castello 35
    03029 Veroli (FR), Italy

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