1 citations · 1 across the 1 of their papers we have counts for
5 papers · 1 filter
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…
Quantum dynamics of elliptic curves
Igor V. Nikolaev
We calculate K-theory of a crossed product -algebra of the noncommutative torus with real multiplication by elliptic curve over a number field . This resul…
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.
Shafarevich-Tate groups of abelian varieties
Igor V. Nikolaev
The Shafarevich-Tate group measures the failure of the Hasse principle for an abelian variety . Using a correspondence between the abelian varieties…
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…