On some Hasse principles over formally real fields

DOI10.1007/BF01214693zbMath0277.15013MaRDI QIDQ1393455

Richard Elman, Alexander Prestel, Tsit-Yuen Lam

Publication date: 1973

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/171986

Mathematics Subject Classification ID

Algebraic theory of quadratic forms; Witt groups and rings (11E81) Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) (12D15) Ordered fields (12J15)

Related Items (47)

Four Dimensional Quadratic Forms OverF(X)Where and a Failure of the Strong Hasse Principle ⋮ Them-ordered real free pro-2-group. Cohomological characterizations^∗ ⋮ Formally real fields with a simple description of the absolute Galois group ⋮ Congruence of Hermitian matrices over some localizations of \(C[z, z^{- 1}\)] ⋮ Minimal forms with respect to function fields of conics ⋮ On trace forms of étale algebras and field extensions ⋮ On the cohomological characterization of real free pro-\(2\)-groups ⋮ Hasse principle for principal homogeneous spaces under classical groups over a field of virtual cohomological dimension at most one ⋮ Classification of Hermitian forms and semisimple groups over fields of virtual cohomological dimension one ⋮ Quadratic modules of polynomials in two variables ⋮ Weakly isotropic quadratic forms under field extensions ⋮ Witt kernels of function field extensions ⋮ Witt rings and almost free pro-2-groups ⋮ Hasse principles and the u-invariant over formally real fields ⋮ The isometry classification of Hermitian forms over division algebras ⋮ Witt rings and Brauer groups under multiquadratic extensions. II ⋮ Isomorphism criteria for Witt rings of real fields ⋮ On the theory of quadratic forms over formally real fields ⋮ Extending orderings on formally real fields ⋮ A Hermitian analogue of the Bröcker-Prestel theorem. ⋮ $R$-equivalence in adjoint classical groups over fields of virtual cohomological dimension $2$ ⋮ Levels of division algebras ⋮ Fed-linked fields and formally real fields satisfying \(B_ 3\) ⋮ Zur Theorie der quadratischen Formen über formalreellen Körpern ⋮ Triple linkage ⋮ Reduzierte quadratische Formen und Semiordnungen reeller Körper ⋮ On SAP fields ⋮ Positive cones on algebras with involution ⋮ Function fields of Pfister forms ⋮ Pfister ideals in Witt rings ⋮ Quadratic forms and profinite 2-groups ⋮ Algebraic systems of quadratic forms of number fields and function fields ⋮ On the integral Hodge conjecture for real varieties. II ⋮ Strongly Anisotropic Involutions on Central Simple Algebras ⋮ Similarity of quadratic forms and half-neighbors ⋮ The Boolean Space of Orderings of a Field ⋮ Automorphisms of pythagorean fields and their witt rings ⋮ Piecewise equivalence of quadratic forms ⋮ A local-global principle for quadratic forms ⋮ Sums of squares in division algebras ⋮ Galois groups of maximal 2-extensions ⋮ Local-global principles for Witt rings ⋮ Biquaternion algebras and quartic extensions ⋮ Stability in Witt Rings ⋮ Formally real fields with prescribed invariants in the theory of quadratic forms ⋮ Pythagoras numbers of fields ⋮ The Reduced Witt Ring of a Formally Real Field

Cites Work

• Euklidische Geometrie ohne das Axiom von Pasch
• Quadratische Semi-Ordnungen und quadratische Formen
• Proof of Krull's intersection theorem for the Witt ring
• Quadratic reciprocity laws
• Pfister forms and \(K\)-theory of fields
• Über eine Klasse pythagoreischer Körper
• Quadratic forms and the u-invariant
• Structure of Witt rings, quotients of abelian group rings and orderings of fields
• Quadratic Forms Over Formally Real Fields and Pythagorean Fields
• The orders of the classical simple groups
• Quadratic forms over arbitrary fields
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