Contents Preface vii Chapter 1. Local Theory 1 1.1. Some lemmas 1 1.2. W-type 5 1.3. Generation of 0{L) 14 1.4. Computations of spinor norms, I 22 1.5. Computations of spinor norms, II 26 1.6. Group structure of 0(X(L/K)) 37 1.7. Reduction formula for 6{X(L/K)), I 38 1.8. Reduction formula for 0(X(L/K)), II 44 1.9. Some computation via reduction formulae 52 1.10. Some notation 57 1.11. Closed forms for 0(X(L/K)) 59 Chapter 2. Global Theory 63 2.0. Introduction 63 2.1. Number of spinor genera in a genus 66 2.2. Representations of spinor genera, codimension 2 74 2.3. Representations of spinor genera, codimension 0 82 Bibliography 85
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