论文标题
在$ k $ - 宇宙二次晶格上
On $k$-universal quadratic lattices over unramified dyadic local fields
论文作者
论文摘要
令$ k $为正整数，让$ f $为$ \ mathbb {q} _2 $带有整数$ \ mathcal {o} _f $的有限不受影响的扩展。 $ \ Mathcal {o} _f $上的积分（经典）二次形式称为$ k $ - umiversal（resp。class。classically$ k $ - umiversal），如果它代表了所有积分（resp。classicclassic）dimension $ k $。在本文中，我们提供了$ k $ - 宇宙和经典$ k $ - 宇宙二次表单上的完整分类，这是$ \ mathcal {o} _f $。结果是根据与二次晶格的约旦分裂相关的基本不变式所述。
Let $k$ be a positive integer and let $F$ be a finite unramified extension of $\mathbb{Q}_2$ with ring of integers $\mathcal{O}_F$. An integral (resp. classic) quadratic form over $\mathcal{O}_F$ is called $k$-universal (resp. classically $k$-universal) if it represents all integral (resp. classic) quadratic forms of dimension $k$. In this paper, we provide a complete classification of $k$-universal and classically $k$-universal quadratic forms over $\mathcal{O}_F$. The results are stated in terms of the fundamental invariants associated to Jordan splittings of quadratic lattices.
