by Markus Rost (6 pages)
J. Ramanujan Math. Soc. 14 (1999), no. 1, 55-63.
Let K/F be a Galois extension of odd degree (Char F not 2) and consider their Wittgroups of quadratic forms. It is well known that the Galois invariant subgroup of W(K) is W(F). A similar statement holds for the sets of Pfister forms.
The notes generalize these matters to arbitrary extensions of odd degree. The method of proof is not very surprising. On the other hand, it seems that there is no reference for this setting.
The results were used in Serre's definition of the H5(Z/2)-invariant for exceptional Jordan algebras. This application gave the original occasion for these notes. For an alternative definition of Serre's invariant using a detailed analysis of Tits' second construction of exceptional Jordan algebras see Lemma 40.1 in The Book of Involutions.
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