✦ LIBER ✦
Invariants of Some Algebraic Curves Related to Drinfeld Modular Curves
✍ Scribed by Ernst-Ulrich Gekeler
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 180 KB
- Volume
- 90
- Category
- Article
- ISSN
- 0022-314X
No coin nor oath required. For personal study only.
✦ Synopsis
We collect some facts about Drinfeld modular curves for a polynomial ring F q [T ] over a finite field F q . These include formulas for the genera, the numbers of cusps and elliptic points, descriptions of the function fields and fields of definition, and other rationality properties. We then show that any series of Drinfeld modular curves of Hecke type X 0 (N k ), where N k # F q [T ] is coprime with T and deg(N k ) Ä , gives rise to an asymptotically optimal series of curves over F q 2 . 2001