Explicit Weil-pairing for Drinfeld modules
نویسندگان
چکیده
The goal of this paper is to define an analogue the Weil-pairing for Drinfeld modules using explicit formulas and deduce its main properties from these formulas. Our result generalizes formula given rank 2 by van der Heiden works as a more explicit, elementary proof Weil-pairing’s existence Heiden.
منابع مشابه
Lehmer Inequality and the Mordell-weil Theorem for Drinfeld Modules
In this paper we prove a special case of the Lehmer inequality for Drinfeld modules which will enable us to extend the results of [6] and [8] to certain infinitely generated fields.
متن کاملThe Lehmer Inequality and the Mordell-weil Theorem for Drinfeld Modules
In this paper we prove several Lehmer type inequalities for Drinfeld modules which will enable us to prove certain Mordell-Weil type structure theorems for Drinfeld modules.
متن کاملSiegel’s Theorem for Drinfeld Modules
We prove a Siegel type statement for finitely generated φsubmodules of Ga under the action of a Drinfeld module φ. This provides a positive answer to a question we asked in a previous paper. We also prove an analog for Drinfeld modules of a theorem of Silverman for nonconstant rational maps of P over a number field.
متن کاملIntegral Points for Drinfeld Modules
We prove that in the backward orbit of a nonpreperiodic (nontorsion) point under the action of a Drinfeld module of generic characteristic there exist at most finitely many points S-integral with respect to another nonpreperiodic point. This provides the answer (in positive characteristic) to a question raised by Sookdeo in [26]. We also prove that for each nontorsion point z there exist at mos...
متن کامل2 2 N ov 2 00 4 DRINFELD MODULAR CURVE AND WEIL PAIRING
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 ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: International Journal of Number Theory
سال: 2021
ISSN: ['1793-7310', '1793-0421']
DOI: https://doi.org/10.1142/s1793042121500809