no. 12
Number Theory
Mass formula for supersingular Drinfeld modules
[Une formule de masse pour les modules de Drinfeld supersinguliers]

Présenté par : Jean-Pierre Serre

Yu, Chia-Fu1 ; Yu, Jing2
1 Department of Mathematics, Columbia University, New York, NY 10027, USA
2 National Center for Theoretical Sciences and Department of Mathematics, National Tsing Hua University, Tsinchu, 30043 Taiwan, ROC
Comptes Rendus. Mathématique, Tome 338 (2004) no. 12, pp. 905-908.

Nous démontrons une « formule de masse » pour les modules de Drinfeld supersinguliers. Cette formule généralise celle obtenue par Gekeler dans le cas de 𝔽 q [T]. La démonstration repose sur un calcul de nombres de Tamagawa.

We generalize Gekeler's mass formula for supersingular Drinfeld modules from rational function fields to arbitrary global function fields. The proof is based on a calculation of Tamagawa numbers.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2004.04.003
Yu, Chia-Fu 1 ; Yu, Jing 2

1 Department of Mathematics, Columbia University, New York, NY 10027, USA
2 National Center for Theoretical Sciences and Department of Mathematics, National Tsing Hua University, Tsinchu, 30043 Taiwan, ROC 
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Yu, Chia-Fu; Yu, Jing. Mass formula for supersingular Drinfeld modules. Comptes Rendus. Mathématique, Tome 338 (2004) no. 12, pp. 905-908. doi : 10.1016/j.crma.2004.04.003. http://www.numdam.org/articles/10.1016/j.crma.2004.04.003/

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[3] Gekeler, E.-U. Sur la géométrie de certaines algèbres de quaternions, Sém. Théor. Nombres Bordeaux, vol. 2, 1990, pp. 143-153

[4] Gekeler, E.-U. On finite Drinfeld modules, J. Algebra, Volume 141 (1991), pp. 187-203

[5] Gekeler, E.-U. On the arithmetic of some division algebras, Comment. Math. Helv., Volume 67 (1992), pp. 316-333

[6] Weil, A. Adèles and Algebraic Groups, Progr. Math., vol. 23, Birkhäuser, Boston, MA, 1982 (With appendices by M. Demazure and T. Ono)

[7] C.-F. Yu, On the mass formula of supersingular abelian varieties with real multiplications. J. Australian Math. Soc., in press

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