Quantum arithmetic
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917867043160064 |
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| author | Nikolaev, Igor V. |
| author_facet | Nikolaev, Igor V. |
| contents | We formalize the quantum arithmetic, i.e. a relationship between number theory and operator algebras. Namely, it is proved that rational projective varieties are dual to the $C^*$-algebras with real multiplication. Our construction fits all axioms of the quantum arithmetic conjectured by Manin and others. Applications to elliptic curves, Shafarevich-Tate groups of abelian varieties and height functions are reviewed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_09148 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantum arithmetic Nikolaev, Igor V. Number Theory Operator Algebras 11M55, 46L85 We formalize the quantum arithmetic, i.e. a relationship between number theory and operator algebras. Namely, it is proved that rational projective varieties are dual to the $C^*$-algebras with real multiplication. Our construction fits all axioms of the quantum arithmetic conjectured by Manin and others. Applications to elliptic curves, Shafarevich-Tate groups of abelian varieties and height functions are reviewed. |
| title | Quantum arithmetic |
| topic | Number Theory Operator Algebras 11M55, 46L85 |
| url | https://arxiv.org/abs/2412.09148 |