Induced orthogonal representations of Galois groups

DOI10.1016/j.jalgebra.2009.07.035zbMath1216.12005OpenAlexW2161535931MaRDI QIDQ2655036

Ivo M. Michailov

Publication date: 22 January 2010

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2009.07.035

zbMATH Keywords

embedding problemGalois extensionmodular groupClifford algebraspinororthogonal representationcorestrictionClifford group

Mathematics Subject Classification ID

Galois cohomology (12G05) Inverse Galois theory (12F12)

Related Items

Parameterizing solutions to any Galois embedding problem over \(\mathbb{Z}/p^n\mathbb{Z}\) with elementary \(p\)-abelian kernel ⋮ On Galois cohomology and realizability of 2-groups as Galois groups. II ⋮ On Galois cohomology and realizability of 2-groups as Galois groups ⋮ Arithmetic properties encoded in the Galois module structure of \(K^\times / K^{\times p^m}\)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On Galois cohomology and realizability of 2-groups as Galois groups
• Four non-abelian groups of order \(p^4\) as Galois groups
• Automatic realization of Galois groups with cyclic quotient of order \(p^n\)
• The Witt invariant of the form \(\text{Tr}(x^ 2)\)
• On the corestriction of central simple algebras
• Relations between \(K_2\) and Galois cohomology
• On the computation of the trace form of some Galois extensions
• Galois module structure of \(p\)th-power classes of extensions of degree \(p\)
• Galois embedding problems with cyclic quotient of order \(p\)
• Brauer type embedding problems
• The corestriction of algebraic structures
• The representation of groups by automorphisms of forms
• $ K$-COHOMOLOGY OF SEVERI-BRAUER VARIETIES AND THE NORM RESIDUE HOMOMORPHISM
• QUADRATIC CORESTRICTION, -EMBEDDING PROBLEMS, AND EXPLICIT CONSTRUCTION
• Orthogonal representations of Galois groups, Stiefel-Whitney classes and Hasse-Witt invariants.
• GALOIS MODULE STRUCTURE OF pTH-POWER CLASSES OF CYCLIC EXTENSIONS OF DEGREE pⁿ
• The Normal Closures of Certain Kummer Extensions
• Trace forms of Galois field extensions in the presence of roots of unity