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.