Drinfeld modular curves have many points
Abstract
Ihara's proof that the reduction of the modular curve $X_0(n)$ at a prime $p$ not dividing $n$ has many points over a quadratic extension is adapted to the drinfeld modular curves $X_0(n)$. In order to do so, some properties of drinfeld modular varieties that have no proof in the literature are proven. The text is more or less self-contained.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- February 2006
- DOI:
- 10.48550/arXiv.math/0602157
- arXiv:
- arXiv:math/0602157
- Bibcode:
- 2006math......2157T
- Keywords:
-
- Mathematics - Algebraic Geometry;
- 11G09;
- 14G50