Let K=F q (T ) be a rational function field and the place given by the degree in T. Let L รK be a finite extension with ramification index not bigger than 2. We show in this paper how the local Ne ron Tate height pairing at on Drinfeld modular curves over K of divisors whose points are defined over
On plane models for Drinfeld modular curves
โ Scribed by So Young Choi; Kuk Jin Hong; Daeyeol Jeon
- Publisher
- Elsevier Science
- Year
- 2006
- Tongue
- English
- Weight
- 124 KB
- Volume
- 119
- Category
- Article
- ISSN
- 0022-314X
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โฆ Synopsis
In this work, we find plane models for certain Drinfeld modular curves X 0 (n) which have better properties than the plane models derived from the usual Drinfeld modular equations. As an application, we construct ring class fields over imaginary quadratic fields by using singular values of generators of the function field of X 0 (n).
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It is known that Drinfeld modular curves can be used to construct asymptotically optimal towers of curves over finite fields. Using reductions of the Drinfeld modular curves X 0 รฐnร, we try to find individual curves over finite fields with many rational points. The main idea is to divide by an Atkin
The purpose of this paper is to decide the conditions under which a CM elliptic curve is modular over its field of definition.