On $k$-universal quadratic lattices over unramified dyadic local fields

Abstract

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.

minor changes in v2; accepted for publication in Journal of Pure and Applied Algebra;40 pages

References in corpus (1)

• On classic $n$-universal quadratic forms over dyadic local fields

Cited by in corpus (3)

• On indefinite $k$-universal integral quadratic forms over number fields
• On classic $n$-universal quadratic forms over dyadic local fields
• On $n$-universal quadratic forms over dyadic local fields