20 citations · 102 across the 71 of their papers we have counts for
71 papers
Drinfeld modules as noncommutative tori
Igor V. Nikolaev
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 i…
Remark on function field analogy
Igor V. Nikolaev
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 numbe…
Birational geometry of quaternions
Igor V. Nikolaev
The Hilbert class field of the quaternion algebra is an algebra such that every two-sided ideal of is principal in . We study the avatars o…
Geometry of division rings
Igor Nikolaev
We prove an analog of Belyi's theorem for the algebraic surfaces. Namely, any non-singular algebraic surface can be defined over a number field if and only it covers the complex pr…
Remark on ordered braid groups
Igor Nikolaev
We recover the Dehornoy order on the braid group from the tracial state on a cluster -algebra associated to the surface of genus …
Comments on a note by M. Waldschmidt
Igor Nikolaev
This note is the follow up to a paper by M. Waldschmidt.