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Number fields as curves over
Igor V. Nikolaev
We study function fields in one variable over the field with one element . It is proved that the Galois extensions of are isomorphic to the curves over $…
Geometry of and Cuntz-Krieger algebras
Igor V. Nikolaev
We study a natural map between projective varieties over the field with one element and the Cuntz-Krieger algebras . Using the -theory of , we calc…
Class number zeta function of imaginary quadratic fields
Igor V. Nikolaev
We introduce a zeta function counting imaginary quadratic number fields by their class numbers. It is proved that such a function is rational depending only on the eight roots of u…
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…
Artin -functions and noncommutative tori
Igor V. Nikolaev
Using the ideas of Deninger, we prove that the Artin -functions coincide with such of the noncommutative tori. This result can be viewed as the Langlands reciprocity for noncomm…
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…