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 Q 2 with ring of integers O F . An integral (resp. classic) quadratic form over 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 O F . The results are stated in terms of the fundamental invariants associated to Jordan splittings of quadratic lattices.