Geodesic
Nonclassical birational models for~$\operatorname{Spec}\mathbb Q$
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 31, Tome 455 (2017), pp. 181-196

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We study generalized subrings of the ring of integers which give birational models for the field of rationals. A homogeneous strengthening of Evdokimov's theorem is proved. An approach to calculation of homotopy groups by means of generalized rings is proposed. 
@article{ZNSL_2017_455_a13,
     author = {A. L. Smirnov},
     title = {Nonclassical birational models for~$\operatorname{Spec}\mathbb Q$},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {181--196},
     publisher = {mathdoc},
     volume = {455},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2017_455_a13/}
}
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A. L. Smirnov. Nonclassical birational models for~$\operatorname{Spec}\mathbb Q$. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 31, Tome 455 (2017), pp. 181-196. http://geodesic.mathdoc.fr/item/ZNSL_2017_455_a13/