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arXiv · 2207.10522

Bounds on Successive Minima of Orders in Number Fields and Scrollar Invariants of Curves

Sameera Vemulapalli
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Abstract

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.

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Sameera Vemulapalli. 2022-07-21. Bounds on Successive Minima of Orders in Number Fields and Scrollar Invariants of Curves. https://arxiv.org/abs/2207.10522

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