111 citations
- Atilim UniversityTR4 papers
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16 papers · 1 filter
Arakelov geometry of Cuntz-Pimsner algebras
Igor V. Nikolaev
We use -theory of the -algebras to study the Arakelov geometry, i.e. a compactification of the arithmetic schemes . In particular, it is proved that…
Non-abelian class field theory and higher dimensional noncommutative tori
Igor V. Nikolaev
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 genera…
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…
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…
Arithmetic complexity revisited
Igor Nikolaev
The arithmetic complexity counts the number of algebraically independent entries in the periodic continued fraction . If $\mathscr{A}_…
Dynamical ideals of non-commutative rings
Igor Nikolaev
A dynamical analog of the prime ideals for simple non-commutative rings is introduced. We prove a factorization theorem for the dynamical ideals. The result is used to classify the…