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.