2019
Том 71
№ 11

All Issues

Zainalov B. R.

Articles: 3
Article (Russian)

First nontrivial group of homologies of simplicial schemes of unimodular frames over the Dedekind ring

Zainalov B. R.

↓ Abstract

Ukr. Mat. Zh. - 2018. - 70, № 9. - pp. 1231-1248

We prove a theorem on generation of the first nontrivial group of homologies of a simplicial scheme of unimodular frames over the Dedekind ring by standard cycles.

Article (Russian)

Preacyclicity over the rings with infinite fields of residues

Zainalov B. R.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2016. - 68, № 2. - pp. 202-216

We consider a simplicial scheme, its geometric realization, and the required properties of the simplicial scheme of unimodal frames and prove both a sufficiently strong theorem on acyclicity for the simplicial scheme of unimodal frames and a theorem stating that the first nontrivial group of homologies is generated by standard cycles over the rings with infinite fields of residues.

Article (Russian)

Homological stabilization for dedekind rings of the arithmetic type

Suslin A. A., Zainalov B. R.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2012. - 64, № 11. - pp. 1464-1476

We study the problem of stabilization in the higher $K$ -theory of rings and improved stabilization. The triviality of the group of standard cycles is established in the case of arithmetic-type rings. Some applications of the obtained results to the problem of homological stabilization are presented.