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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.12660 |
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| _version_ | 1866917987843309568 |
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| author | Grzegorczyk, Ivona Suarez, Ricardo |
| author_facet | Grzegorczyk, Ivona Suarez, Ricardo |
| contents | In this paper we construct complex tori, denoted by $S_{\mathbb{B}_{1,p,q}}$, as quotients of tensor products of Cayley--Dickson algebras, denoted $\mathbb{B}_{1,p,q}=\mathbb{C}\otimes \mathbb{H}^{\otimes p}\otimes \mathbb{O}^{\otimes q}$, with their integral subrings. We then show that these complex tori have endomorphism rings of full rank and are isogenous to the direct sum of $2^{2p+3q}$ copies of an elliptic curve $E$ of $j$-invariant $1728$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_12660 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Complex tori constructed from Cayley-Dickson algebras Grzegorczyk, Ivona Suarez, Ricardo Algebraic Geometry In this paper we construct complex tori, denoted by $S_{\mathbb{B}_{1,p,q}}$, as quotients of tensor products of Cayley--Dickson algebras, denoted $\mathbb{B}_{1,p,q}=\mathbb{C}\otimes \mathbb{H}^{\otimes p}\otimes \mathbb{O}^{\otimes q}$, with their integral subrings. We then show that these complex tori have endomorphism rings of full rank and are isogenous to the direct sum of $2^{2p+3q}$ copies of an elliptic curve $E$ of $j$-invariant $1728$. |
| title | Complex tori constructed from Cayley-Dickson algebras |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2504.12660 |