Determination of quadratic lattices by local structure and sublattices of codimension one

Abstract

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