Local isomorphism classes of fractional ideals of orders in étale algebras
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913735035060224 |
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| author | Marseglia, Stefano |
| author_facet | Marseglia, Stefano |
| contents | We study the local isomorphism classes, also known as genera or weak equivalence classes, of fractional ideals of orders in étale algebras. We provide a classification in terms of linear algebra objects over residue fields. As a by-product, we obtain a recursive algorithm to compute representatives of the classes, which vastly outperforms previously known methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_18571 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Local isomorphism classes of fractional ideals of orders in étale algebras Marseglia, Stefano Number Theory Rings and Algebras 16H10, 11Y40 We study the local isomorphism classes, also known as genera or weak equivalence classes, of fractional ideals of orders in étale algebras. We provide a classification in terms of linear algebra objects over residue fields. As a by-product, we obtain a recursive algorithm to compute representatives of the classes, which vastly outperforms previously known methods. |
| title | Local isomorphism classes of fractional ideals of orders in étale algebras |
| topic | Number Theory Rings and Algebras 16H10, 11Y40 |
| url | https://arxiv.org/abs/2311.18571 |