Brauer Groups and Witt Groups
The final three chapters of this book will focus on connections and applications of the theory presented so far to some important concerns in mathematics especially the theory of algebras and quadratic forms. This chapter recalls the Brauer group, the Brauer-Wall group, and the Witt groups. We shall see that these concepts are closely related to each other and to the themes of this book. The links are provided by the invariants of quadratic forms, and in particular by the Arf invariant (already defined in Chapters 7C and 10D in the free case). In view of the extensive literature on these topics, proofs or sketches of proofs are provided only when they seemed not available in appropriately explicit form. The constructions are presented in the generality of commutative rings and then illustrated in the classical situations: over the real and complex numbers, and local and global fields.
KeywordsCommutative Ring Hyperbolic Space Clifford Algebra Symmetric Bilinear Form Global Field
Unable to display preview. Download preview PDF.