Preface ....................................................... vii
Chapter 1. Local Theory ......................................... 1
1.1. Some lemmas ............................................. 1
1.2. W-type .................................................. 5
1.3. Generation of O(L) ..................................... 14
1.4. Computations of spinor norms, I ........................ 22
1.5. Computations of spinor norms, II ....................... 26
1.6. Group structure of θ(X(L/K)) ........................... 37
1.7. Reduction formula for θ(X(L/K)), I ..................... 38
1.8. Reduction formula for θ(X(L/K)), II .................... 44
1.9. Some computation via reduction formulae ................ 52
1.10. Some notation .......................................... 57
1.11. Closed forms for θ(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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