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JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. 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

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.

UDC: 512.5

Received: 11.01.2017


 English version:
Journal of Mathematical Sciences (New York), 2018, 234:2, 237–247


© Steklov Math. Inst. of RAS, 2024