Determination of Quadratic Lattices by Local Structure and Sublattices of Codimension One

For definite quadratic lattices over the rings of integers of algebraic number fields, it is shown that lattices are determined up to isometry by their local structure and sublattices of codimension 1. In particular, a theorem of Yoshiyuki Kitaoka for $\mathbb{Z}$-lattices is generalized to definite lattices over algebraic number fields