Igor V. Nikolaev

collaborators

4 papers

math.NT2026

Geometry of $F_{1}$ and Cuntz-Krieger algebras

Igor V. Nikolaev

We study a natural map between projective varieties $V (F_{1})$ over the field with one element and the Cuntz-Krieger algebras $O_{A}$ . Using the $K$ -theory of $O_{A}$ , we calc…

math.NT2026

Arakelov geometry of Cuntz-Pimsner algebras

Igor V. Nikolaev

We use $K$ -theory of the $C^{*}$ -algebras to study the Arakelov geometry, i.e. a compactification of the arithmetic schemes $V \to S p ec Z$ . In particular, it is proved that…

math.NT2026

Class number zeta function of imaginary quadratic fields

Igor V. Nikolaev

We introduce a zeta function counting imaginary quadratic number fields by their class numbers. It is proved that such a function is rational depending only on the eight roots of u…

math.NT2025

Non-abelian class field theory and higher dimensional noncommutative tori

Igor V. Nikolaev

We study a relation between the Drinfeld modules and the even dimensional noncommutative tori. A non-abelian class field theory is developed based on this relation. Explicit genera…

Geometry of F1​ and Cuntz-Krieger algebras

Arakelov geometry of Cuntz-Pimsner algebras

Class number zeta function of imaginary quadratic fields

Non-abelian class field theory and higher dimensional noncommutative tori

Geometry of $F_{1}$ and Cuntz-Krieger algebras