Arakelov geometry of Cuntz-Pimsner algebras
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911655546322944 |
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| author | Nikolaev, Igor V. |
| author_facet | Nikolaev, Igor V. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_17063 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Arakelov geometry of Cuntz-Pimsner algebras Nikolaev, Igor V. Number Theory Algebraic Geometry Operator Algebras 11M55, 14G40, 46L85 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. |
| title | Arakelov geometry of Cuntz-Pimsner algebras |
| topic | Number Theory Algebraic Geometry Operator Algebras 11M55, 14G40, 46L85 |
| url | https://arxiv.org/abs/2406.17063 |