2 2 N ov 2 00 4 DRINFELD MODULAR CURVE AND WEIL PAIRING
نویسنده
چکیده
In this paper we describe the compactification of the Drin-feld modular curve. This compactification is analogous to the compact-ification of the classical modular curve given by Katz and Mazur. We show how the Weil pairing on Drinfeld modules that we defined in earlier work gives rise to a map on the Drinfeld modular curve. We introduce the Tate-Drinfeld module and show how this describes the formal neighbourhood of the scheme of cusps of the Drinfeld modular curve.
منابع مشابه
On the degree of modular parametrizations over function fields
Let E be an elliptic curve over FqðTÞ with conductor N N: Let Y : X0ðNÞ-E be the modular parametrization by the Drinfeld modular curve of level N: Assuming that E is a strong Weil curve we prove upper and lower bounds on deg Y: These bounds are the analogs of well-known (partially conjectural) bounds in the case of rational numbers. r 2002 Elsevier Science (USA). All rights reserved.
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