Dirichlet's theorem in Diophantine approximation is known to be closely related to geometry of the hyperbolic plane. In this paper we consider approximation in the setting of number fields and study relation between systems of linear forms and geometry of products of symmetric spaces.
"Diophantine approximation in number fields and geometry of products of symmetric spaces." J. Math. Soc. Japan 73 (3) 885 - 932, July, 2021. https://doi.org/10.2969/jmsj/81358135