Mass formula for supersingular Drinfeld modules

Chia-Fu Yu; Jing Yu

doi:10.1016/j.crma.2004.04.003

Number Theory

Mass formula for supersingular Drinfeld modules

Presented by: Jean-Pierre Serre

Chia-Fu Yu ¹; Jing Yu 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

Comptes Rendus. Mathématique, Volume 338 (2004) no. 12, pp. 905-908.

Abstract
Résumé

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.

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.

Received: 2004-01-17
Accepted: 2004-04-05
Published online: 2004-05-12

DOI: 10.1016/j.crma.2004.04.003

Author's affiliations:

Chia-Fu Yu ¹; Jing Yu 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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     title = {Mass formula for supersingular {Drinfeld} modules},
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Chia-Fu Yu; Jing Yu. Mass formula for supersingular Drinfeld modules. Comptes Rendus. Mathématique, Volume 338 (2004) no. 12, pp. 905-908. doi : 10.1016/j.crma.2004.04.003. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.04.003/

References
Cited by

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

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

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

[6] A. Weil 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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