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 
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/
@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},
     year = {2017},
     volume = {455},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2017_455_a13/}
}
TY  - JOUR
AU  - A. L. Smirnov
TI  - Nonclassical birational models for $\operatorname{Spec}\mathbb Q$
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2017
SP  - 181
EP  - 196
VL  - 455
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2017_455_a13/
LA  - ru
ID  - ZNSL_2017_455_a13
ER  - 
%0 Journal Article
%A A. L. Smirnov
%T Nonclassical birational models for $\operatorname{Spec}\mathbb Q$
%J Zapiski Nauchnykh Seminarov POMI
%D 2017
%P 181-196
%V 455
%U http://geodesic.mathdoc.fr/item/ZNSL_2017_455_a13/
%G ru
%F ZNSL_2017_455_a13

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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.

[1] Sh. Haran, “Non-additive geometry”, Compositio Math., 143 (2007), 618–688 | DOI | MR | Zbl

[2] N. Durov, New approach to Arakelov geometry, 16 Apr. 2007, arXiv: 0704.2030v1[math.AG]

[3] J.-P. Serre, Algebraic Groups and Class Fields, Springer-Verlag, 1988 | MR | Zbl

[4] A. L. Smirnov, “Obobschennye podkoltsa arifmeticheskikh kolets”, Zap. nauchn. semin. POMI, 349, 2007, 211–241

[5] S. A. Evdokimov, “Dokazatelstvo kongruents-gipotezy dlya obobschennykh kolets”, Zap. nauchn. semin. POMI, 443, 2016, 91–94 | MR

[6] A. L. Smirnov, “Binarnoe proektivnoe prostranstvo”, Zap. nauchn. semin. POMI, 365, 2009, 208–224 | Zbl

[7] D. A. Klarner, R. Rado, “Arithmetic properties of certaine recurcively defined sets”, Pacific J. Math., 53:2 (1974), 445–463 | DOI | MR | Zbl

[8] J. Lagarias, “The $3x+1$ problem and its generalizations”, Amer. Math. Monthly, 92:1 (1985), 3–23 | DOI | MR | Zbl

[9] S. Burckel, “Functional equations associated with congruential functions”, Theor. Comput. Sci., 123 (1994), 397–406 | DOI | MR | Zbl

[10] J. H. Conway, “Unpredictable iterations”, Proc. Number Theory, 1972, 49–52 | MR | Zbl

[11] J. Lagarias, The $3x+ $ Problem: an Annotated Bibliography (1963–1999) (sorted by author), 11 Jan. 2011, arXiv: math/0309224v13[math.NT]