Pfister forms and K-theory of fields

“…The fact that Q a is a 2-splitting variety for a follows from the theory of Pfister quadratic forms; [32], chapter 4 for instance. (In fact, Q a is a generic 2-splitting variety for a following [9], [15]. )…”

Section: Theorem 54 [43]mentioning

confidence: 99%

Voevodsky’s proof of Milnor’s conjecture

Morel

1998

Bull. Amer. Math. Soc.

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“…By [3, Proposition 4.6] there exist Pfister forms ρ ∈ P n−1 F , η ∈ P 2 F , and r ∈Ḟ such that σ ρ ⊗ η and π ρ ⊗ r . (This result in [3] is only stated for linkage of two Pfister forms of the same dimension, but it also applies to two Pfister forms of different dimension. The proof carries over without change.)…”

Section: Some Remarks On Forms Of Heightmentioning

confidence: 99%

On quadratic forms of height two and a theorem of Wadsworth

Hoffmann¹

1996

Trans. Amer. Math. Soc.

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Abstract. Let ϕ and ψ be anisotropic quadratic forms over a field F of characteristic not 2. Their function fields F (ϕ) and F (ψ) are said to be equivalent (over F ) if ϕ ⊗ F (ψ) and ψ ⊗ F (ϕ) are isotropic. We consider the case where dim ϕ = 2 n and ϕ is divisible by an (n − 2)-fold Pfister form. We determine those forms ψ for which ϕ becomes isotropic over F (ψ) if n ≤ 3, and provide partial results for n ≥ 4. These results imply that if F (ϕ) and F (ψ) are equivalent and dim ϕ = dim ψ, then ϕ is similar to ψ over F . This together with already known results yields that if ϕ is of height 2 and degree 1 or 2, and if dim ϕ = dim ψ, then F (ϕ) and F (ψ) are equivalent iff F (ϕ) and F (ψ) are isomorphic over F .

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Pfister forms and K-theory of fields

Cited by 122 publications

References 4 publications

An exact sequence for K_∗^M∕2 with applications to quadratic forms

An exact sequence for K_∗^M∕2 with applications to quadratic forms

Voevodsky’s proof of Milnor’s conjecture

On quadratic forms of height two and a theorem of Wadsworth

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Pfister forms and K-theory of fields

Cited by 122 publications

References 4 publications

An exact sequence for K∗M∕2 with applications to quadratic forms

An exact sequence for K∗M∕2 with applications to quadratic forms

Voevodsky’s proof of Milnor’s conjecture

On quadratic forms of height two and a theorem of Wadsworth

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Product

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An exact sequence for K_∗^M∕2 with applications to quadratic forms

An exact sequence for K_∗^M∕2 with applications to quadratic forms