In this paper, we give an algebraic description of the set of algebraic points of any degree over  on hyperelliptic curves . This result extends a result of Bruin [1].

degree of algebraic points, rational points, algebraic extensions.

Received: February 1, 2023; Accepted: March 29, 2023; Published: April 13, 2023

How to cite this article: EL Hadji SOW, Moussa Fall and Moustapha CAMARA, Algebraic points on the curves  JP Journal of Geometry and Topology 29(1) (2023), 29-34. http://dx.doi.org/10.17654/0972415X23003

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References:

[1] N. Bruin, On powers as sums of two cubes, International Algorithmic Number Theory Symposium, Springer, Berlin, Heidelberg, 2000.
[2] P. A. Griffiths, Introduction to algebraic curves, Translations of mathematical monographs, American Mathematical Society, Providence, Vol. 76, 1989.
[3] E. H. Sow, P. M. Sarr and O. Sall, Points algébriques de degrés au-plus 5 sur la courbed’ équation affine  International Journal of Development Research 11(12) (2021), 52435-52439.
[4] O. Sall, M. Fall and C. M. Coly, Points algébriques de degré donné sur la courbe d’équation affine  International Journal of Development Research 6(11) (2016), 10295-10300.