20 citations · 102 across the 71 of their papers we have counts for
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Riemann surfaces and AF-algebras
Igor Nikolaev
For a generic set in the Teichmueller space, we construct a covariant functor with the range in a category of the AF-algebras; the functor maps isomorphic Riemann surfaces to the s…
On a Teichmueller functor between the categories of complex tori and the Effros-Shen algebras
Igor Nikolaev
A covariant functor from the category of the complex tori to the category of the Effros-Shen algebras is constructed. The functor maps isomorphic complex tori to the stably isomorp…
Remark on the rank of elliptic curves
Igor Nikolaev
A covariant functor on the elliptic curves with complex multiplication is constructed. The functor takes values in the noncommutative tori with real multiplication. A conjecture on…
On a desingularization of the moduli space of noncommutative tori
Igor Nikolaev
It is shown that the moduli space of the noncommutative tori A admits a natural desingularization by the group Ext (A, A). Namely, we prove that the moduli space of pairs (A, Ext (…