20 citations · 102 across the 71 of their papers we have counts for
25 papers · 1 filter
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…
Comments on a note by M. Waldschmidt
Igor Nikolaev
This note is the follow up to a paper by M. Waldschmidt.
Class field towers and minimal models
Igor V. Nikolaev
We use the notion of an Etesi -algebra to prove that the real class field towers are always finite.
Remark on Faltings theorem
Igor Nikolaev
We prove Faltings Finiteness Theorem using Rieffel's classification of the noncommutative tori.