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| Main Author: | |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2207.10522 |
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Table of 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.