Number Theory
Mass formula for supersingular Drinfeld modules
Comptes Rendus. Mathématique, Volume 338 (2004) no. 12, pp. 905-908.

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:
Accepted:
Published online:
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
@article{CRMATH_2004__338_12_905_0,
     author = {Yu, Chia-Fu and Yu, Jing},
     title = {Mass formula for supersingular {Drinfeld} modules},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {905--908},
     publisher = {Elsevier},
     volume = {338},
     number = {12},
     year = {2004},
     doi = {10.1016/j.crma.2004.04.003},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2004.04.003/}
}
TY  - JOUR
AU  - Yu, Chia-Fu
AU  - Yu, Jing
TI  - Mass formula for supersingular Drinfeld modules
JO  - Comptes Rendus. Mathématique
PY  - 2004
SP  - 905
EP  - 908
VL  - 338
IS  - 12
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2004.04.003/
DO  - 10.1016/j.crma.2004.04.003
LA  - en
ID  - CRMATH_2004__338_12_905_0
ER  - 
%0 Journal Article
%A Yu, Chia-Fu
%A Yu, Jing
%T Mass formula for supersingular Drinfeld modules
%J Comptes Rendus. Mathématique
%D 2004
%P 905-908
%V 338
%N 12
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2004.04.003/
%R 10.1016/j.crma.2004.04.003
%G en
%F CRMATH_2004__338_12_905_0
Yu, Chia-Fu; Yu, Jing. 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. http://www.numdam.org/articles/10.1016/j.crma.2004.04.003/

[1] Drinfeld, V. Elliptic modules, Math. USSR-Sb., Volume 23 (1976), pp. 561-592

[2] Gekeler, E.-U. Sur les classes d'idéaux des ordres de certains corps gauches, C. R. Acad. Sci. Paris Sér. I Math., Volume 309 (1989), pp. 577-580

[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

Cited by Sources: