Let $k$ be a function field over finite field $\mathbb{F}_q$ and
let $A$ be the ring consisting of elements of $k$ regular away from a fixed place $\infty$ of $k$.
Let $\phi$ be a Drinfeld $A$-module over a finite field $L$.
We define the Frobenius torus of $\phi$ by similar way with the case of elliptic curves
and study the structure when the rank of $\phi$ equal to $2,3$.
For Drinfeld $A$-module $\phi$ over $K$ where $K/k$ is a finite separable extension,
we define the $v$-adic representations of $Gal(K^s/K)$.
When the rank of $\phi$ equal to $1$, we define the cyclotomic characters
and discuss the case of $sgn$-normalized rank $1$ Drinfeld module
and the special case of Carlitz module.

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