Some Analytic and Arithmetic Properties of Integral Models of Algebraic Tori

We study the properties of integral models of algebraic tori defined over number fields. We give some analytic arithmetic properties of the models of infinite type and find generators of algebras that serve as integral models for algebraic tori. We also study the ring of integer-valued p-adic polynomials, present their factorial properties, and consider algebras of integer-valued functions for low-dimensional and quasi-split tori, for which we determine the generators. In conclusion, some further research is briefly outlined.