I. Nikolaev

activity

20242026

collaborators

6 papers

math.GT2026

K-theory of Etesi C*-algebras

Igor V. Nikolaev

We study the $C^{*}$ -algebra $E_{M}$ of a smooth 4-dimensional manifold $M$ introduced by GÃ¡bor Etesi. It is proved that the $E_{M}$ …

math.OA2025

Jones Index Theorem revisited

Andrey Yu. Glubokov, Igor V. Nikolaev

We prove the Jones Index Theorem using the K-theory of a cluster $C^{*}$ -algebra of the Riemann sphere with two boundary components.

math.NT2025

Birational geometry of quaternions

Igor V. Nikolaev

The Hilbert class field of the quaternion algebra $B$ is an algebra $H (B)$ such that every two-sided ideal of $B$ is principal in $H (B)$ . We study the avatars o…

math.NT2025

Quantum dynamics of elliptic curves

Igor V. Nikolaev

We calculate K-theory of a crossed product $C^{*}$ -algebra of the noncommutative torus with real multiplication by elliptic curve $E (K)$ over a number field $K$ . This resul…

math.AG2025

Trace cohomology revisited

Igor V. Nikolaev

We use a cohomology theory coming from the canonical trace on a C*-algebra of the projective variety to prove an analog of the Riemann Hypothesis for the Kuga-Sato varieties over f…

math.NT2024

Class field towers and minimal models

Igor V. Nikolaev

We use the notion of an Etesi $C^{*}$ -algebra to prove that the real class field towers are always finite.