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Zapiski Nauchnykh Seminarov POMI, 2017, Volume 455, Pages 181–196 (Mi znsl6414)  
Nonclassical birational models for $\operatorname{Spec}\mathbb Q$

A. L. Smirnov

St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, St. Petersburg, Russia
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Abstract: 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.
Key words and phrases: generalized ring, generalized scheme, arithmetic curve, singularity, cusp, node, birational, model, field with one element, homotopy groups.
Funding agency Grant number
Russian Foundation for Basic Research 16-01-00750
Received: 11.01.2017
English version:
Journal of Mathematical Sciences (New York), 2018, Volume 234, Issue 2, Pages 237–247
DOI: https://doi.org/10.1007/s10958-018-3999-2
Document Type: Article
UDC: 512.5
Language: Russian
Citation: A. L. Smirnov, “Nonclassical birational models for $\operatorname{Spec}\mathbb Q$”, Problems in the theory of representations of algebras and groups. Part 31, Zap. Nauchn. Sem. POMI, 455, POMI, St. Petersburg, 2017, 181–196; J. Math. Sci. (N. Y.), 234:2 (2018), 237–247
Citation in format AMSBIB
\Bibitem{Smi17}
\by A.~L.~Smirnov
\paper Nonclassical birational models for~$\operatorname{Spec}\mathbb Q$
\inbook Problems in the theory of representations of algebras and groups. Part~31
\serial Zap. Nauchn. Sem. POMI
\yr 2017
\vol 455
\pages 181--196
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6414}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2018
\vol 234
\issue 2
\pages 237--247
\crossref{https://doi.org/10.1007/s10958-018-3999-2}
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