Some Aspects of the Algebraic Theory of Quadratic Forms

DOI10.1007/978-1-4614-7488-3_7zbMath1282.11025OpenAlexW2165125753MaRDI QIDQ5397109

Raman Parimala

Publication date: 19 February 2014

Published in: Quadratic and Higher Degree Forms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-1-4614-7488-3_7

zbMATH Keywords

function fieldsGalois cohomologyinvariantsquadratic formsnumber fields

Mathematics Subject Classification ID

Algebraic theory of quadratic forms; Witt groups and rings (11E81) Spectral theory; trace formulas (e.g., that of Selberg) (11F72)

Cites Work

• The \(u\)-invariant of the function fields of \(p\)-adic curves
• An exact sequence for \(K^M_*/2\) with applications to quadratic forms
• Patching over fields
• Applications of patching to quadratic forms and central simple algebras
• Cohomologische Invarianten quadratischer Formen
• Isotropy of quadratic forms over function fields of \(p\)-adic curves
• Patching and local-global principles for homogeneous spaces over function fields of \(p\)-adic curves
• On sums of squares and on elliptic curves over function fields
• Quadratic forms and the u-invariant. I
• Artin's Conjecture on Zeros of $p$-Adic Forms
• Fields of u-Invariant 2 r + 1
• A Hasse principle for two dimensional global fields.
• SIMPLE ALGEBRAS AND QUADRATIC FORMS
• Pythagoras numbers of fields
• Zur Darstellung von -1 Als Summe von Quadraten in Einem Körper
• Rational points in Henselian discrete valuation rings
• Fields of \(u\)-invariant \(9\)
• Hasse principles for higher-dimensional fields
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