Geodesic
Arithmetic properties of three-dimensional algebraic tori
Zapiski Nauchnykh Seminarov POMI, Integral lattices and finite linear groups, Tome 116 (1982), pp. 102-107 
B. È. Kunyavskii. Arithmetic properties of three-dimensional algebraic tori. Zapiski Nauchnykh Seminarov POMI, Integral lattices and finite linear groups, Tome 116 (1982), pp. 102-107. http://geodesic.mathdoc.fr/item/ZNSL_1982_116_a10/
@article{ZNSL_1982_116_a10,
     author = {B. \`E. Kunyavskii},
     title = {Arithmetic properties of three-dimensional algebraic tori},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {102--107},
     year = {1982},
     volume = {116},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1982_116_a10/}
}
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We compute the Shafarevich-Tate group, the kernel of the weak approximation and the Manin groups of three-dimensional algebraic tori defined over an algebraic number field. A minimal example of a torus with fractional Tamagawa number is constructed. A criterion for the validity of the Hasse norm principle for extensions of degree four of an algebraic number field is given.