论文标题
在温和晶格中的最小向量的基础
Bases of minimal vectors in tame lattices
论文作者
论文摘要
由痕迹配对与温和循环数字字段的行为的动机，我们介绍了驯服晶格的概念。给定一个任意的非平常晶格$ \ MATHCAL {l} $，我们构建了一个由$ \ MATHCAL {l} $的全级子范围的参数家族$ \ {\ Mathcal {\ Mathcal {\ Mathcal {\ Mathcal {\ Mathcal {\ Mathcal {\ Mathcal {l}_α\} $，只要$ \ nathcal {l} $ nim a niim a niim是tame a niim a nim a iniim a iniim a inim向量。此外，对于家族中的每个$ \ Mathcal {l}_α$，都明确构造了最小向量的基础。
Motivated by the behavior of the trace pairing over tame cyclic number fields, we introduce the notion of tame lattices. Given an arbitrary non-trivial lattice $\mathcal{L}$ we construct a parametric family of full-rank sub-lattices $\{\mathcal{L}_α\}$ of $\mathcal{L}$ such that whenever $\mathcal{L}$ is tame each $\mathcal{L}_α$ has a basis of minimal vectors. Furthermore, for each $\mathcal{L}_α$ in the family a basis of minimal vectors is explicitly constructed.
