Odd quadratic orders and real $j$-invariants
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909271901339648 |
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| author | Zarhin, Yuri G. |
| author_facet | Zarhin, Yuri G. |
| contents | Let $O$ be an order of odd discriminant $D$ in an imaginary quadratic field $K$. Let $Cl(O)$ be the group of proper $O$-ideals and $Cl(O)[2]$ the kernel of multiplication by $2$ in $Cl(O)$. We describe explicitly the group $Cl(O)[2]$. In particular, we prove that its order is
$2^{s_D-1}$ where $s_D$ is the number of prime divisors of $D$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_16703 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Odd quadratic orders and real $j$-invariants Zarhin, Yuri G. Number Theory Algebraic Geometry 11R11, 11R29, 11R65, 11G15, 14H52 Let $O$ be an order of odd discriminant $D$ in an imaginary quadratic field $K$. Let $Cl(O)$ be the group of proper $O$-ideals and $Cl(O)[2]$ the kernel of multiplication by $2$ in $Cl(O)$. We describe explicitly the group $Cl(O)[2]$. In particular, we prove that its order is $2^{s_D-1}$ where $s_D$ is the number of prime divisors of $D$. |
| title | Odd quadratic orders and real $j$-invariants |
| topic | Number Theory Algebraic Geometry 11R11, 11R29, 11R65, 11G15, 14H52 |
| url | https://arxiv.org/abs/2407.16703 |