Characterization of Minimal Pfister Neighbors via Rost Projectors
نویسندگان
چکیده
Let φ be an anisotropic 9-dimensional quadratic form over a field (of characteristic ̸= 2). We show that the projective quadric given by φ possesses a Rost projector if and only if φ is a Pfister neighbor. The following consequence of this result gives the initial step in the construction [10] of the filed with the u-invariant 9: if φ is not a Pfister neighbor and the Schur index of its even Clifford algebra is at least 4, then φ stays anisotropic over the function field of any 9-dimensional form non-similar to φ.
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