Igor V. Nikolaev

activity

20232026

most citedNon-abelian class field theory and higher dimensional noncommutative tori

1 citations · 1 across the 5 of their papers we have counts for

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math.NT2026

Number fields as curves over $F_{1}$

Igor V. Nikolaev

We study function fields in one variable over the field with one element $F_{1}$ . It is proved that the Galois extensions of $Q$ are isomorphic to the curves over $…

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

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…

Number fields as curves over F1​

Geometry of F1​ and Cuntz-Krieger algebras

Class number zeta function of imaginary quadratic fields

Number fields as curves over $F_{1}$

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