CONSTRUCTION OF SELF-DUAL INTEGRAL NORMAL BASES IN ABELIAN EXTENSIONS OF FINITE AND LOCAL FIELDS

DOI10.1142/S1793042110003654zbMath1239.11140arXiv1007.0326OpenAlexW3099246619MaRDI QIDQ3067878

Erik Jarl Pickett

Publication date: 13 January 2011

Published in: International Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1007.0326

zbMATH Keywords

local fieldsfinite fieldsGalois moduleself-dual normal basissquare-root of the inverse different

Mathematics Subject Classification ID

Separable extensions, Galois theory (12F10) Galois theory (11S20) Integral representations (11S23) Integral representations of finite groups (20C10) Structure theory for finite fields and commutative rings (number-theoretic aspects) (11T30) Integral representations related to algebraic numbers; Galois module structure of rings of integers (11R33) Class field theory; (p)-adic formal groups (11S31)

Related Items (5)

Iwasawa theory and p-adic L-functions over ${\mathbb Z}_{p}^{2}$-extensions ⋮ Finding normal bases over finite fields with prescribed trace self-orthogonal relations ⋮ Trace self-orthogonal relations of normal bases ⋮ Construction of self-dual normal bases and their complexity ⋮ Self-dual integral normal bases and Galois module structure

Cites Work

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• The Galois structure of the square root of the inverse different
• A method for constructing a self-dual normal basis in odd characteristic extension fields
• Explicit construction of self-dual integral normal bases for the square-root of the inverse different
• The Galois structure of the trace form in extensions of odd prime degree
• Integral Galois module structure of some Lubin-Tate extensions
• The Jacobson radical of commutative group rings
• Constructing normal bases in finite fields
• Forms in Odd Degree Extensions and Self-Dual Normal Bases
• CONSTRUCTION OF POLYNOMIALS IRREDUCIBLE OVER A FINITE FIELD WITH LINEARLY INDEPENDENT ROOTS
• ON NORMAL BASES OF A FINITE FIELD
• Galois module structure in weakly ramified 3-extensions

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