On PAC Extensions and Scaled Trace Forms

2007/05/24 by Lior Bary‐Soroker, Lior Bary-Soroker, Bary-Soroker, Lior +2 · 1 citation
Computer Science · Mathematics · #Finite Group Theory Research #Rings, Modules, and Algebras #math.NT #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.0705.3573

10 pages; added results on prime-to-p extensions, removed the condition on the countability of the fields

arxiv created 2007/08/29 · arxiv updated 2009/12/01

Abstract

Any non-degenerate quadratic form over a Hilbertian field (e.g., a number field) is isomorphic to a scaled trace form. In this work we extend this result to more general fields. In particular, prosolvable and prime-to-p extensions of a Hilbertian field. The proofs are based on the theory of PAC extensions.

Cited by

• Irreducible values of polynomials

Related

• Companion Forms Over Totally Real Fields, II
• On number fields with equivalent integral trace forms
• Companion forms over totally real fields
• Relative Trace Formula and Uniform non-vanishing of Central L-values of Hilbert Modular Forms
• Explicit determination of images of Galois representations attached to Hilbert modular forms