Spinor norm for skew-hermitian forms over quaternion algebras

Abstract

We complete all local spinor norm computations for quater-nionic skew-hermitian forms over the field Qof rational num-bers. This can be used to compute the number of classes in a genus of skew-hermitian lattices of rank 2or larger over a max-imal order in a quaternion algebra Dover Qin many cases, e.g., when Dramifies at infinity. Examples are provided