On the coincidence of standard and canonical integral models of an arbitrary algebraic torus over a number field

Algebraic tori occupy a special place among linear algebraic groups. An algebraic torus can be defined over an arbitrary field but if a ground field belongs to an arithmetic type one can additionally consider schemes over this field's ring of integers which are linked to the original tori and called their integral models. Néron model and Voskresenskiĭ model are most well-known among them. There exists a broad range of problems dealing with the construction of these models and the research of their properties. This paper is dedicated to the research of some important integral models of algebraic tori over number fields, namely, standard and canonical integral models. Finally, the coincidence of these two models for an arbitrary algebraic torus is proven.