Galois lattices and reductions of algebraic tori

In this paper we construct the minimal integral model of a finite type of an algebraic torus defined over a complete non-Archimedean extension of an algebraic number field. The main problem is to study this model in the case of the ramified splitting field. We describe the models of quasi-split tori, norm tori and tori of low dimension. We also calculate the reduction of these models.