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

$\Phi$ be a Drinfeld $\mathbf{F}\_{q}[T]$-module of rank 2, over a finite field $L$. Let $P\_{\Phi}(X)=$ $X^{2}-cX+\mu P^{m}$ ($c$ an element of $\mathbf{F}\_{q}[T],$ $\mu$ be a non-vanishing element of $$, $m$ the degree of the extension $L$ over the field $$ and $P$ the $\mathbf{F}\_{q}[T]$-characteristic of $$ 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 $\mathbf{F}\_{q}[T]$-module $L^{\Phi}$ induced by $\Phi$ over $L$. Our main result is analogue to that of Deuring (see \cite{Deuring}) for elliptic curves : Let M=\frac{\mathbf{F}\_{q}[T]}{I\_{1}}\oplus \frac{\mathbf{F}\_{q}[T]}{% I\_{2}}, where $I\_{1}=(i\_{1})$,$I\_{2}=(i\_{2})$ ($i\_{1}$, $i\_{2}$ being two polynomials of $\mathbf{F}\_{q}[T]$) such that : $i\_{2}\mid (c-2)$. Then there exists an ordinary Drinfeld $\mathbf{F}\_{q}[T]$-module $\Phi$ over $L$ of rank 2 such that : $L^{\Phi}$ $\simeq M$. To cite this article: Mohamed-Saadbouh Mohamed-Ahmed, C. R. Acad. Sci. Paris, Ser. I ... (...).