Rigid elements, valuations, and realization of Witt rings

DOI10.1016/0021-8693(87)90057-3zbMath0629.10016OpenAlexW1967710359MaRDI QIDQ1093666

Jón Kr. Arason, Richard Elman, Bill Jacob

Publication date: 1987

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

Full work available at URL: https://doi.org/10.1016/0021-8693(87)90057-3

zbMATH Keywords

isomorphismsvaluationcharacteristic not tworigid elementsrealization theorem for Witt rings

Mathematics Subject Classification ID

Quadratic forms over general fields (11E04) General binary quadratic forms (11E16) Valued fields (12J10) Field extensions (12F99)

Related Items (24)

Detecting fast solvability of equations via small powerful Galois groups ⋮ On Witt Rings of Quaternion Algebras over 1-Hilbert Fields ⋮ Compatible valuations and generalized Milnor 𝐾-theory ⋮ A Galois-theoretic characterization of \(p\)-adically closed fields ⋮ A recursive description of the maximal pro-2 Galois group via Witt rings ⋮ Commuting-liftable subgroups of Galois groups. II ⋮ Witt equivalence of function fields over global fields ⋮ Witt rings and almost free pro-2-groups ⋮ Totally real rigid elements and F_π-henselian valuation rings ⋮ Recent progress on definability of Henselian valuations ⋮ Witt equivalence of fields: A survey with a special emphasis on applications of hyperfields ⋮ Quadratic forms over dyadic valued fields. II: Relative rigidity and Galois cohomology ⋮ Abelian-by-central Galois groups of fields. II: Definability of inertia/decomposition groups ⋮ Realizing dyadic factors of elementary type Witt rings and pro-2 Galois groups ⋮ Witt equivalence of function fields of conics ⋮ On the 3-Pfister Number of Quadratic Forms ⋮ Abelian subgroups of pro-$p$ Galois groups ⋮ On graphs and valuations. ⋮ A Note on the Quaternion Group as Galois Group ⋮ Valuations and diameters of Milnor \(K\)-rings ⋮ Unnamed Item ⋮ The metabelian birational -adic section conjecture for varieties ⋮ Homomorphisms of multiplicative groups of fields preserving algebraic dependence ⋮ The Graded Witt Ring and Galois Cohomology. II

Cites Work

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• On the structure of Pythagorean fields
• Fans, real valuations, and hereditarily-Pythagorean fields
• Succinct and representational Witt rings
• On the extension of real places
• Valuation Rings and Rigid Elements in Fields
• The Graded Witt Ring and Galois Cohomology. II
• Witt Rings and Brauer Groups Under Multiquadratic Extensions, I
• Quadratic Forms Over Formally Real Fields and Pythagorean Fields

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