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Diallo, Mohamadou Mor Diogou. (1404). Describing families of algebraic points of given degree on a hyperelliptic curve. سامانه مدیریت نشریات علمی, 6(1), 83-91. doi: 10.22098/jfga.2025.16876.1147
Mohamadou Mor Diogou Diallo. "Describing families of algebraic points of given degree on a hyperelliptic curve". سامانه مدیریت نشریات علمی, 6, 1, 1404, 83-91. doi: 10.22098/jfga.2025.16876.1147
Diallo, Mohamadou Mor Diogou. (1404). 'Describing families of algebraic points of given degree on a hyperelliptic curve', سامانه مدیریت نشریات علمی, 6(1), pp. 83-91. doi: 10.22098/jfga.2025.16876.1147
Diallo, Mohamadou Mor Diogou. Describing families of algebraic points of given degree on a hyperelliptic curve. سامانه مدیریت نشریات علمی, 1404; 6(1): 83-91. doi: 10.22098/jfga.2025.16876.1147

Describing families of algebraic points of given degree on a hyperelliptic curve

Journal of Finsler Geometry and its Applications
دوره 6، شماره 1، مهر 2025، صفحه 83-91    اصل مقاله (325.98 K)
نوع مقاله: Original Article
شناسه دیجیتال (DOI): 10.22098/jfga.2025.16876.1147
نویسنده
Mohamadou Mor Diogou Diallo*
Department of Mathematics, Assane Seck University of Ziguinchor Ziguinchor, Senegal
چکیده
In this paper, we give a parametrization of the set of algebraic points of degree at most l over Q on the hyperelliptic curve
y2 = x(x2 + x - 4)(x2 - x + 45)
This curve was studied by Bruin and Flynn in [4] where the heights explicitly described the set of rational points, i.e. C(1)(Q). Drawing on the work of Arnth-Jensen and Flynn based on [2] and one of Abel-Jacobi's fundamental theorems in [1, 8], we extend the results of [4] to algebraic points of any degree which we denote C(l)(Q).
کلیدواژه‌ها
Mordell-Weill group؛ Rational Points؛ Jacobian؛ Galois Conjugate؛ Linear Systems
مراجع
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3. A. Borel and J. P. Serre, Le th´eor´eme de Riemann-Roch, Bultin de la Soci´et´e math´ematiques de france, 86 (1958), 97-136.
4. N. Bruin and E. V. Flynn, Exhibiting SHA [2] on hyperelliptic Jacobians, Journal of Number Theory, 118 (2) (2006), 266-291.
5. M. Coppens and G. Martens, Secant spaces and Clifford’s theorem, Compositio Mathematica, 78 (2) (1991), 193-212.
6. M. Fall, M. M. D.Diallo and C. M. Coly, Algebraic Points of any Given Degree on the Affine Curves y2 = x(x + 2p)(x + 4p)(x2 - 8p2), Journal of Contemporary Applied Mathematics, 13 (1) (2023), 11-23.
7. G. Faltings, Finiteness Theorems for Abelian Varieties over Number Fields, Arithmetic Geometry, 1986.
8. P. A. Griffiths, Introduction to algebraic curves: Translations of mathematical monographs, American Mathematical Society, Providence, RI, 76 (1989).
9. M. Gromov and M. A. Shubin, The Riemann-Roch theorem for elliptic operators, IM Gelfand Seminar part, 1 (1993).
10. M. M. D. Diallo, Explicit family of algebraic points of given degree of the curve family Cq, Journal of Advanced Mathematical Studies, 17 (4) (2024), 444-450.
11. P. Vojta, Siegel’s theorem in the compact case, Annals of Mathematics, 133 (3) (1991),509-548. 

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