20 citations · 102 across the 71 of their papers we have counts for
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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…
Noncommutative geometry of elliptic surfaces
Igor Nikolaev
We recast elliptic surfaces over the projective line in terms of the non-commutative tori and one-parameter families of the periodic continued fractions. The correspondence is used…
On tea, donuts and non-commutative geometry
Igor Nikolaev
As many will agree, it feels good to complement a cup of tea by a donut or two. This sweet relationship is also a guiding principle of non-commutative geometry known as Serre Theor…
Trace cohomology revisited
Igor V. Nikolaev
We use a cohomology theory coming from the canonical trace on a C*-algebra of the projective variety to prove an analog of the Riemann Hypothesis for the Kuga-Sato varieties over f…
Remark on Weil's conjectures
Igor Nikolaev
We introduce a cohomology theory for a class of projective varieties over a finite field coming from the canonical trace on a C*-algebra attached to the variety. Using the cohomolo…
Remark on Serre -algebras
Igor Nikolaev
We study non-commutative algebraic geometry of Artin, Serre and Tate in terms of the operator algebras. Namely, we define the Serre -algebra of a projective va…