Quadratic Forms over Fields I: Foundations
نویسنده
چکیده
1. Four equivalent definitions of a quadratic form 2 2. Action of Mn(K) on n-ary quadratic forms 4 3. The category of quadratic spaces 7 4. Orthogonality in quadratic spaces 9 5. Diagonalizability of Quadratic Forms 11 6. Isotropic and hyperbolic spaces 13 7. Witt’s theorems: statements and consequences 15 8. Orthogonal groups, reflections and the proof of Witt Cancellation 17 8.1. The orthogonal group of a quadratic space 17 8.2. Reflection through an anisotropic vector 18 8.3. Proof of Witt Cancellation 19 9. The Witt Ring 20 9.1. The Grothendieck-Witt Ring 20 10. Additional Exercises 22 References 24
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