On the coincidence of standard and canonical integral models of an arbitrary algebraic torus over a number field
Integral models play a central role in the arithmetic of algebraic groups. Among the linear algebraic groups, the tori serve as a stepping stone for the general case. The integral models of algebraic tori over \(p\)-adic local fields are relatively well understood, after the works of Néron et al. As for the global case over number fields, there are at least two models. One is the standard model from \textit{V. E. Voskresenskiĭ} et al. [St. Petersbg. Math. J. 14, No. 1, 46--70 (2003; Zbl 1060.20042); translation from Algebra Anal. 14, No. 1, 46--70 (2002)]. The other one is the canonical model from \textit{V. E. Voskresenskiĭ} [Algebraic groups and their birational invariants. Transl. from the original Russsian manuscript by Boris Kunyavskii. Rev. version of `Algebraic tori', Nauka 1977. Providence, RI: American Mathematical Society (1998; Zbl 0974.14034)], \S 10. The author proves in this paper that these two integral models agree for any algebraic tori over a number field.
scientific article; zbMATH DE number 6818285