Integral models of algebraic tori over number fields

An algebraic torus can be defined over an arbitrary field but if a ground field has an arithmetic type one can additionally consider schemes over the ring of integers of this field. These schemes are linked to the original tori and called integral models. Néron model and Voskresenskiĭ model are most well-known among them. This paper is dedicated to the research of main integral models of algebraic tori over number fields and to the comparison of their properties. A particular family of the maximal algebraic tori without an affect of semisimple groups of type $B_n$ is taken into account as a polygon for the realization of the previously researched constructions.