B. Kahn and A. Laghribi: A second descent problem for quadratic forms

kahn@math.jussieu.fr, laghribi@agel.ucl.ac.be

Submission: 2002, Jan 21

Let F be a field of characteristic different from 2. We discuss a new descent problem for quadratic forms, complementing one previously studied by the two authors. More precisely, we conjecture that for any quadratic form q over F and any form phi over the function field F(q) of q which is defined over F up to Witt equivalence, there exists a quadratic form psi over F such that phi= psi_{F(q)} up to Witt equivalence and dim(psi) is at most 2dim(phi). We prove this conjecture for dim(phi) at most 3 and any q, and get partial results for dim(phi) between 4 and 6. We also give other related results.

2000 Mathematics Subject Classification:

Keywords and Phrases: quadratic form, Galois cohomology, rationality

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