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arXiv · 2406.17063

Arakelov geometry of Cuntz-Pimsner algebras

Igor V. Nikolaev
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Abstract

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

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Igor V. Nikolaev. 2024-06-24. Arakelov geometry of Cuntz-Pimsner algebras. https://doi.org/10.1002/mana.70158

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