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Arakelov Geometry of Cuntz–Pimsner Algebras

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  • Igor V. Nikolaev

Abstract

We use K$K$‐theory of the C∗$C^*$‐algebras to study the Arakelov geometry, i.e., a compactification of the arithmetic schemes V→SpecZ$V\rightarrow \operatorname{Spec} \nobreakspace \mathbf {Z}$. In particular, it is proved that the Picard group of V$V$ is isomorphic to the K0$K_0$‐group of a Cuntz–Pimsner algebra associated with V$V$. We apply this result to the finiteness problem for the algebraic varieties over number fields.

Suggested Citation

  • Igor V. Nikolaev, 2026. "Arakelov Geometry of Cuntz–Pimsner Algebras," Mathematische Nachrichten, Wiley Blackwell, vol. 299(7), pages 1549-1555, July.
    • Handle: RePEc:bla:mathna:v:299:y:2026:i:7:p:1549-1555
    DOI: 10.1002/mana.70158
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