Self-dual integral normal bases and Galois module structure
نویسندگان
چکیده
منابع مشابه
Cohomological Invariants for G - Galois Algebras and Self - Dual Normal Bases
We define degree two cohomological invariants for GGalois algebras over fields of characteristic not 2, and use them to give necessary conditions for the existence of a self–dual normal basis. In some cases (for instance, when the field has cohomological dimension ≤ 2) we show that these conditions are also sufficient.
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Let F be a field containing a primitive pth root of unity, and let U be an open normal subgroup of index p of the absolute Galois group GF of F . We determine the structure of the cohomology group H(U, Fp) as an Fp[GF /U ]-module for all n ∈ N. Previously this structure was known only for n = 1, and until recently the structure even of H(U, Fp) was determined only for F a local field, a case se...
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Let F/E be a finite Galois extension of fields with abelian Galois group Γ. A self-dual normal basis for F/E is a normal basis with the additional property that TrF/E(g(x), h(x)) = δg,h for g, h ∈ Γ. Bayer-Fluckiger and Lenstra have shown that when char(E) 6= 2, then F admits a self-dual normal basis if and only if [F : E] is odd. If F/E is an extension of finite fields and char(E) = 2, then F ...
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متن کاملExplicit Construction of Self-Dual Integral Normal Bases for the Square-Root of the Inverse Different
Let K be a finite extension of Qp, let L/K be a finite abelian Galois extension of odd degree and let OL be the valuation ring of L. We define AL/K to be the unique fractional OL-ideal with square equal to the inverse different of L/K. For p an odd prime and L/Qp contained in certain cyclotomic extensions, Erez has described integral normal bases for AL/Qp that are self-dual with respect to the...
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ژورنال
عنوان ژورنال: Compositio Mathematica
سال: 2013
ISSN: 0010-437X,1570-5846
DOI: 10.1112/s0010437x12000851