Ulf Rehmann

Coincidence Site Modules in 3-Space

The coincidence site lattice (CSL) problem and its generalization to ℤ-modules in Euclidean 3-space is revisited, and various results and conjectures are proved in a unified way, by using maximal orders in quaternion algebras of class number 1 over real algebraic number fields.

A variant of a theorem by Springer

The theorem in question gives a sufficient condition for a quadratic space over a local ring R to contain a hyperbolic plane over R.

SPLITTING PATTERNS AND TRACE FORMS

The splitting pattern of a quadratic form q over a fieldk consists of all distinct Witt indices that occur for q over extension fields of k. In small dimensions, the complete list of splitting patterns of quadratic forms i s known. We show that all splitting patterns of quadratic forms of dimension at most n ine can be realized by trace forms.