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the a_s are only invariants mod 2! (or equivalently, the image of the determinant in K*/K*^2 is invariant). For instance, take x^2+y^2 over Q and do x->x+y y->x-y. In general classifying quadratic forms involves contributions from all degrees of Galois cohomology (where K*/K*^2 is only a H^1) :)
May 4, 2025, 10:15 PM
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"text": "the a_s are only invariants mod 2! (or equivalently, the image of the determinant in K*/K*^2 is invariant). For instance, take x^2+y^2 over Q and do\nx->x+y\ny->x-y.\nIn general classifying quadratic forms involves contributions from all degrees of Galois cohomology (where K*/K*^2 is only a H^1) :)",
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