Birational geometry of quaternions
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866909667576250368 |
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| author | Nikolaev, Igor V. |
| author_facet | Nikolaev, Igor V. |
| contents | The Hilbert class field of the quaternion algebra $B$ is an algebra $\mathscr{H}(B)$ such that every two-sided ideal of $B$ is principal in $\mathscr{H}(B)$. We study the avatars of $B$ and $\mathscr{H}(B)$, i.e. algebraic surfaces attached to the quaternion algebras. It is proved that the avatar of $\mathscr{H}(B)$ is obtained from the avatar of $B$ by a birational map. We apply this result to the function field analogy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_06555 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Birational geometry of quaternions Nikolaev, Igor V. Number Theory Algebraic Geometry Operator Algebras 12E15, 32J15, 46L85 The Hilbert class field of the quaternion algebra $B$ is an algebra $\mathscr{H}(B)$ such that every two-sided ideal of $B$ is principal in $\mathscr{H}(B)$. We study the avatars of $B$ and $\mathscr{H}(B)$, i.e. algebraic surfaces attached to the quaternion algebras. It is proved that the avatar of $\mathscr{H}(B)$ is obtained from the avatar of $B$ by a birational map. We apply this result to the function field analogy. |
| title | Birational geometry of quaternions |
| topic | Number Theory Algebraic Geometry Operator Algebras 12E15, 32J15, 46L85 |
| url | https://arxiv.org/abs/2212.06555 |