Montes Algorithm In Function Fields

Let $A=k[t]$ be the polynomial ring over the perfect field $k$ and $f \in A[x]$ be a monic irreducible separable polynomial. Denote by $F/k$ the function field determined by $f$ and consider a given non-zero prime ideal $\mathfrak{p}$ of $A$. The Montes algorithm determines a new representation, so called OM-representation, of the prime ideals of the (finite) maximal order of $F$ lying over $\mathfrak{p}$. This yields a new representation of places of function fields.  In this talk we summarize briefly some applications of this new representation; that are the computation of the genus, the computation of the maximal order, and the improvement of the computation of Riemann-Roch spaces.