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Curves on Frobenius classical surfaces in $\mathbb{P}^{3}$ over finite fields

Volume 205 / 2022

Elena Berardini, Jade Nardi Acta Arithmetica 205 (2022), 323-340 MSC: Primary 11G20; Secondary 14G05, 14H50, 14J70. DOI: 10.4064/aa211118-12-9 Published online: 17 October 2022


We give an upper bound on the number of rational points on an irreducible curve $C$ of degree $\delta $ defined over a finite field $\mathbb F_q$ lying on a Frobenius classical surface $S$ embedded in $\mathbb P^3$. This leads us to investigate arithmetic properties of curves lying on surfaces. In a certain range of $\delta $ and $q$, our result improves all other known bounds in the context of space curves.


  • Elena BerardiniLTCI, Télécom Paris
    Institut polytechnique de Paris
    F-91120 Palaiseau, France
  • Jade NardiUniversité Rennes
    CNRS, IRMAR – UMR 6625
    F-35000 Rennes, France

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