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Formally Real Fields RealClosed Fields and Pythagorean Fields
Quadratic Forms under Transcendental Extensions
Pfister Forms and Function Fields
Special Topics in Quadratic Forms
Special Topics on Invariants
anisotropic anisotropic form anisotropic over F assume binary form Chapter clearly closed field construction Corollary CSGA defined denote dim q division algebra element equation equivalent euclidean exists extension K/F extension of F F is formally F is nonreal F-algebra F-form fact field extension field F finite field form over F form q formally real field function field graded algebra hence homomorphism hyperbolic implies induction integer isometry isomorphism Lemma Let F Let q multiplicative n-fold Pfister form nonreal fields nonzero notation number field orthogonal Pfister form Pfister neighbor polynomial prime ideal Proof Proposition prove Pythagoras number pythagorean field q is isotropic quadratic extension quadratic form quadratic form theory quadratic space quadratically closed quaternion algebras real-closed field result splits square classes squares in F subform subgroup Theorem torsion u-invariant unique vector Witt ring write Wt(F zero