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Titlebook: Introduction to Quadratic Forms; O. Timothy O’Meara Book 20001st edition Springer-Verlag Berlin Heidelberg 2000 Arithmetic Theory of Field

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Quadratic Forms over Dedekind Domainse present chapter is to state the nature of this problem in modern terminology and in the general setting of an arbitrary Dedekind domain. Our second purpose is to develop some technique in this general situation. The more interesting results must wait until we specialize to the fields of number the
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Integral Theory of Quadratic Forms over Global FieldsWe conclude this book by introducing the genus and the spinor genus of a lattice on a quadratic space over a global field, and by studying the relation between these two new objects and the class. We shall use these relations to obtain sufficient conditions under which two lattices are in the same class.
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