Grégory Berhuy: On hermitian trace forms over hilbertian fields (to appear in Math.Z.)

Submission: 2000, Apr. 10

We show that every non-degenerate quadratic form of even rank over a hilbertian field k, which is not isomorphic to the hyperbolic plane, is isomorphic to $\mathrm{Tr}_{E/k}(\lambda x x^\sigma)$, where $E/k$ is a separable field extension, $\sigma$ is a $k$-linear involution on $E$ and $\lambda$ is a $\sigma$-symmetric element. We also show that an even-dimensional quadratic form $q$ over an hilbertian field of stability index at most 2 is Witt-equivalent to $\mathrm{Tr}_{E/k}(x x^\sigma)$ if and only if $q$ is positive.

1991 Mathematics Subject Classification:

Keywords and Phrases:

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