Let $A$ and $B$ two matrices in $GL_{n}(K[[\pi]])$, regular semisimple on $GL_{n}(K((\pi)))$, with $K$ an algebraically closed field of characteristic zero .
We suppose that they have the same characteristic polynomial $\chi\in K[[\pi]][t]$.
Let $d$ be the valuation of the discriminant of $\chi$.
We suppose that $A=B ~[\pi^{d+1}]$, do we have that $A$ and $B$ are conjugate by an element of $GL_{n}(K[[\pi]])$?
