Endomorphism rings and isogenies classes for Drinfeld <i>A</i>-modules of rank 2 over finite fields

Mohamed-Saadbouh Mohamed-Ahmed

doi:10.1016/j.crma.2006.10.026

Algebraic Geometry

Endomorphism rings and isogenies classes for Drinfeld A-modules of rank 2 over finite fields

Presented by: Christophe Soulé

Mohamed-Saadbouh Mohamed-Ahmed ¹

¹ Département de mathématiques, université du Maine, avenue Olivier-Messiaen, 72085 Le Mans cedex 9, France

Comptes Rendus. Mathématique, Volume 343 (2006) no. 11-12, pp. 737-740.

Abstract
Résumé

For a Drinfeld module of rank 2, we discuss many analogy points with elliptic curves. More precisely, we study the characteristic polynomial of a Drinfeld module of rank 2 and use it to calculate the number of isogeny classes for such modules.

Pour un module de Drinfeld de rang 2, on étudie plusieurs points d'analogie avec les courbes elliptiques. Plus précisément, on étudie la charactéristique polynômiale d'un module de Drinfeld de rang 2 et en l'utilisant, on calcule le nombre de classes d'isogénies d'un module de Drinfeld de rang 2 sur un corps fini.

Received: 2006-03-01
Accepted: 2006-10-27
Published online: 2006-12-01

DOI: 10.1016/j.crma.2006.10.026

Author's affiliations:

Mohamed-Saadbouh Mohamed-Ahmed ¹

¹ Département de mathématiques, université du Maine, avenue Olivier-Messiaen, 72085 Le Mans cedex 9, France

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Mohamed-Saadbouh Mohamed-Ahmed. Endomorphism rings and isogenies classes for Drinfeld A-modules of rank 2 over finite fields. Comptes Rendus. Mathématique, Volume 343 (2006) no. 11-12, pp. 737-740. doi : 10.1016/j.crma.2006.10.026. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.10.026/

References
Cited by

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[2] Bruno Angles One some subring of Ore polynomials connected with finite Drinfeld modules, J. Algebra, Volume 181 (1996) no. 2, pp. 507-522

[3] V.G. Drinfeld Modules elliptiques, Math. USSR-Sb., Volume 94(136) (1974), pp. 594-627 (656)

[4] E.-U. Gekeler, B.A. Snyder, Drinfeld modules over finite fields, in: Drinfeld Modules, Modular Schemes and Application, Alden-Biesen, 1996

[5] D. Goss Basic Structures of Function Field Arithmetic, Ergebnise der Mathematik und ihrer Grenzgebiete, vol. 35, Springer, 2006

[6] J.-K. Yu Isogenies of Drinfeld modules over finite fields, J. Number Theory, Volume 54 (1995) no. 1, pp. 161-171

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