Witt rings and Brauer groups under multiquadratic extensions. II

DOI10.1016/0021-8693(82)90102-8zbMath0492.10015OpenAlexW2087009135MaRDI QIDQ1167755

Daniel B. Shapiro, Adrian R. Wadsworth, Jean-Pierre E. Tignol

Publication date: 1982

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-8693(82)90102-8

zbMATH Keywords

complexeshomology groupsmultiquadratic extensionquaternion homomorphismWitt ring of anisotropic quadratic forms

Mathematics Subject Classification ID

Quadratic forms over general fields (11E04) Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) (12D15) Brauer groups of schemes (14F22) General binary quadratic forms (11E16)

Related Items (11)

Examples of non-rational varieties of adjoint groups ⋮ Quaternion fields inside Pythagorean closure ⋮ Similarity of quadratic forms and related problems ⋮ The graded Witt group kernel of biquadratic extensions in characteristic two ⋮ On the Rost divisibility of henselian discrete valuation fields of cohomological dimension 3 ⋮ Unnamed Item ⋮ Quadratic forms over dyadic valued fields. II: Relative rigidity and Galois cohomology ⋮ On the Brauer group complex for a multiquadratic field extension ⋮ Quadratic Forms ⋮ Orthogonal involutions on central simple algebras and function fields of Severi-Brauer varieties ⋮ Trace forms of central simple algebras

Cites Work

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• Quadratic forms under algebraic extensions
• Cohomologische Invarianten quadratischer Formen
• On multiples of round and Pfister forms
• Function fields of Pfister forms
• Pfister ideals in Witt rings
• On some Hasse principles over formally real fields
• Algebraic \(K\)-theory and quadratic forms. With an appendix by J. Tate
• Pfister forms and \(K\)-theory of fields
• Spaces of Orderings IV
• Corps a Involution Neutralises par une Extension Abelienne Elementaire
• Witt Rings and Brauer Groups Under Multiquadratic Extensions, I
• Piecewise equivalence of quadratic forms
• Structure of Witt Rings and Quotients of Abelian Group Rings
• Division algebras of degree 4 and 8 with involution
• Quadratic forms over arbitrary fields
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