Name
Mihran Papikian
TITLE:
The number of rational points on Drinfeld modular varieties over finite
fields
ABSTRACT:
Drinfeld and Vladut proved that Drinfeld modular curves have many rational
points over the quadratic extensions of finite fields compared to their genera;
see [VD] and [MV]. We propose a conjectural generalization of this result to the
higher dimensional Drinfeld modular varieties [D]. Using some deep results of
Harder and Laumon, we prove a theorem which provides evidence for the
conjecture.
References
[D]: V. Drinfeld, Elliptic modules, Math. Sbornik 94
(1974), 594-627.
[MV]: Yu. Manin and S. Vladut, Linear codes and modular curves, J. Sov.
Math. 30 (1985), 2611-2643.
[VD]: S. Vladut and V. Drinfeld, The number of points of an algebraic curve,
Funct. Anal. Appl. 17 (1983), 53-54.