Sur la Structure de A-module de Drinfeld de rang 2

2006/06/17 by Mohamed Saadbouh Mohamed Ahmed, Ahmed, Mohamed Saadbouh Mohamed
Mathematics · #Algebraic Geometry and Number Theory #Finite Group Theory Research #Advanced Algebra and Geometry

paper · doi:10.48550/arxiv.math/0606417

Abstract

Φ be a Drinfeld F_q[T]-module of rank 2, over a finite field L. Let P_Φ(X)= X²-cX+μP^m (c an element of F_q[T], μ be a non-vanishing element of % F_q, m the degree of the extension L over the field % F_q[T]/P, and P the F_q[T]-characteristic of % L and d the degree of the polynomial P) the characteristic polynomial of the Frobenius F of L. We will be interested in the structure of finite F_q[T]-module L^Φ induced by Φ over L. Our main result is analogue to that of Deuring (see \citeDeuring) for elliptic curves : Let M=\fracF_q[T]I_1⊕ \fracF_q[T]% I_2, where I_1=(i_1), I_2=(i_2) (i_1, i_2 being two polynomials of F_q[T]) such that : i_2| (c-2). Then there exists an ordinary Drinfeld F_q[T]-module Φ over L of rank 2 such that : L^Φ ≃ M. To cite this article: Mohamed-Saadbouh Mohamed-Ahmed, C. R. Acad. Sci. Paris, Ser. I ... (...).

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