Bounds on Successive Minima of Orders in Number Fields and Scrollar Invariants of Curves
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arXiv
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866913927918518272 |
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| author | Vemulapalli, Sameera |
| author_facet | Vemulapalli, Sameera |
| contents | Orders and fractional ideals in number fields provide interesting examples of lattices. We ask: what lattices arise from orders in number fields? We prove that all nontrivial multiplicative constraints on successive minima of orders come from multiplication. Moreover, inspired by a conjecture of Lenstra, for infinitely many positive integers $n$ (including all $n < 18$), we explicitly determine all multiplicative constraints on successive minima of orders in degree $n$ number fields. We also prove analogous results for scrollar invariants of curves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_10522 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Bounds on Successive Minima of Orders in Number Fields and Scrollar Invariants of Curves Vemulapalli, Sameera Number Theory Algebraic Geometry 11H50 (Primary) 11H06, 11P21, 14H05 (Secondary) Orders and fractional ideals in number fields provide interesting examples of lattices. We ask: what lattices arise from orders in number fields? We prove that all nontrivial multiplicative constraints on successive minima of orders come from multiplication. Moreover, inspired by a conjecture of Lenstra, for infinitely many positive integers $n$ (including all $n < 18$), we explicitly determine all multiplicative constraints on successive minima of orders in degree $n$ number fields. We also prove analogous results for scrollar invariants of curves. |
| title | Bounds on Successive Minima of Orders in Number Fields and Scrollar Invariants of Curves |
| topic | Number Theory Algebraic Geometry 11H50 (Primary) 11H06, 11P21, 14H05 (Secondary) |
| url | https://arxiv.org/abs/2207.10522 |