Zobrazeno 1 - 10
of 303
pro vyhledávání: '"Nikolaev, Igor"'
Autor:
Nikolaev, Igor V.
Let $k$ be a number field and $V(k)$ an $n$-dimensional projective variety over $k$. We use the $K$-theory of a $C^*$-algebra $A_V$ associated to $V(k)$ to define a height of points of $V(k)$. The corresponding counting function is calculated and we
Externí odkaz:
http://arxiv.org/abs/2408.12020
Autor:
Nikolaev, Igor V.
We use $K$-theory of the $C^*$-algebras to study the Arakelov geometry, i.e. a compactification of the arithmetic schemes $V\to Spec ~\mathbf{Z}$. In particular, it is proved that the Picard group of $V$ is isomorphic to the $K_0$-group of a Cuntz-Pi
Externí odkaz:
http://arxiv.org/abs/2406.17063
Autor:
Nikolaev, Igor V.
We recast the local factors of the Hasse-Weil zeta function at infinity in terms of the Cuntz-Pimsner algebras. The nature of such factors is an open problem studied by Deninger and Serre.
Comment: 8 pages
Comment: 8 pages
Externí odkaz:
http://arxiv.org/abs/2404.12179
Autor:
Nikolaev, Igor V.
Using the ideas of Deninger, we prove that the Artin $L$-functions coincide with such of the noncommutative tori. This result can be viewed as the Langlands reciprocity for noncommutative tori.
Comment: 9 pages. arXiv admin note: text overlap wi
Comment: 9 pages. arXiv admin note: text overlap wi
Externí odkaz:
http://arxiv.org/abs/2312.17638
Autor:
Nikolaev, Igor V.
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 generators of the Galois extensions are constructed.
Comment: 13 pages,
Comment: 13 pages,
Externí odkaz:
http://arxiv.org/abs/2309.05779
Autor:
Nikolaev, Igor V.
The Drinfeld module is a tool of the explicit class field theory for the function fields. We first observe a similarity of such modules with the noncommutative tori, and then use it to develop an explicit class field theory for the number fields. The
Externí odkaz:
http://arxiv.org/abs/2306.06416
Autor:
Nikolaev, Igor V.
We study the analogy between number fields and function fields in one variable over finite fields. The main result is an isomorphism between the Hilbert class fields of class number one and a family of the function fields $\mathbf{F}_q(C)$ over a des
Externí odkaz:
http://arxiv.org/abs/2302.12632
Autor:
Nikolaev, Igor
The Hilbert class field of the quaternion algebra $B$ is an algebra $\mathscr{H}(B)$ such that every two-sided ideal of $B$ is principal in $\mathscr{H}(B)$. We study the avatars of $B$ and $\mathscr{H}(B)$, i.e. algebraic surfaces attached to the qu
Externí odkaz:
http://arxiv.org/abs/2212.06555