Introduction To Quadratic Forms Over Fields

By T. Lam. 2004

949 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2e1432778120c6ff5e9b7f2cb844ed8ea9503e9d

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In Applied Mathematics

1. Ján Minác
2. Ido Efrat
3. K. Wickelgren
4. K. Ormsby
5. David W. Lewis
6. Sergey Norin
7. Hamed Hatami
8. Jesse Leo Kass

In Mathematical Physics

1. Ido Efrat
2. K. Ormsby
3. K. Wickelgren
4. Jesse Leo Kass
5. Ján Minác
6. P. Hu
7. Paul Balmer
8. David W. Lewis

Citations in the corpus

• Applications of patching to quadratic forms and central simple algebras (2008, methodology): “By [Lam05℄, VI.1.9(2), q′ = q̃ ⊥ tq̃ isanisotropi over K̂, the fra tion eld of T̂ .”
• Spectra, spectra, spectra – Tensor triangular spectra versus Zariski spectra of endomorphism rings (2010, background): “This ring is classical and its quotient W(F ) = GW(F )/h by the 2-dimensional hyperbolic plane h = 1, −1 is the even more classical Witt ring ; see Lam [18].”
• Quaternion Algebras and the Algebraic Legacy of Hamilton's Quaternions (2006, background): “For a proof of this theorem of Albert, see [29], theorem 4.”
• Local-global principles for torsors over arithmetic curves (2011, methodology): “By Witt decomposition ([Lam05, Theorem I.4.1]), every regular form q is Witt equivalent to an anisotropic form; i.e. q = qa ⊥ qh with qa anisotropic and qh hyperbolic.”
• Quotients of absolute Galois groups which determine the entire Galois cohomology (2009, background): “is not a maximal pro-pGalois group also when p= 2. Indeed, assume G∼= G F (2) for some field F. Then F×/(F×)2 ∼= H1(G) ∼= (Z/2)2. As Gis torsion free, Fhas no orderings [Bec74]. By a theorem of Kneser [Lam05], non-isotropic QUOTIENTS OF ABSOLUTE GALOIS GROUPS 13 quadratic forms over F have dimension ”
• Cohomological Invariants: Exceptional Groups and Spin Groups (2009, background): “6-dimensional form x of determinant 1. As 1 is a square in k, x is an Albert form, i.e., x =hdi( 0 1 02) for 2-Pfister forms 1, 2 and some d2 k◊ [ Lam05 , XII.2.13].”
• The class of Eisenbud–Khimshiashvili–Levine is the local A1-Brouwer degree (2016, background): “By [Lam05, Remark 3.14], the pair (Q̃, β̃) is isomorphic to an orthogonal sum of a symmetric bilinear form defined over k and a sum of symmetric bilinear forms defined by Gram matrices of the form (19) ( a(y) 1 1 0 ) for a(y) ∈ k[y], so it is enough to prove the lemma in the special case of a…”
• Convergence of the Motivic Adams Spectral Sequence (2011, background): “A cell spectrum of weakly finite type is equivalent to a cell spectrum of finite type.”