论文标题
连续数字字段中的订单和滚动曲线不变的最小值的界限
Bounds on Successive Minima of Orders in Number Fields and Scrollar Invariants of Curves
论文作者
论文摘要
数量字段中的订单和分数理想提供了有趣的晶格示例。我们问：数字字段中的订单产生了哪些晶格？我们证明，对连续的订单最小值的所有非平凡的乘法约束都来自乘法。此外，受Lenstra的猜想的启发，对于无限的许多正整数$ n $（包括所有$ n <18 $），我们明确确定了对$ n $数字字段中连续的最小订单的所有乘法约束。我们还证明了曲线不变的曲线结果。
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.
