Galois Algebras , Hasse Principle and Induction – Restriction Methods
نویسندگان
چکیده
Let k be a field of characteristic 6= 2, and let L be a Galois extension of k with group G. Let us denote by qL : L × L → k the trace form, defined by qL(x, y) = TrL/k(xy). Let (gx)g∈G be a normal basis of L over k. We say that this is a self–dual normal basis if qL(gx, hx) = δg,h. If the order of G is odd, then L always has a self–dual normal basis over k (cf. [1]). This is no longer true in general if the order of G is even; some partial results are given in [2].
منابع مشابه
BANFF WORKSHOP ON “DIOPHANTINE METHODS, LATTICES, AND ARITHMETIC THEORY OF QUADRATIC FORMS”: TITLES AND ABSTRACTS 1. Hour-long talks
Eva Bayer-Fluckiger (École Polytechnique Fédérale de Lausanne) Title: Galois algebras, Hasse principle and induction-restriction methods Abstract: The aim of this talk is to survey old and new results on self-dual normal bases and more generally invariants of Galois algebras. Particular attention will be given to local-global principles. Some of the results make use of an inductionrestriction m...
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