On a conjecture of Izhboldin on similarity of quadratic forms

  • Detlev W. Hoffmann

    6, route de Gray 25030 Besancon Cedex, France
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Abstract

In his paper \itMotivic equivalence of quadratic forms, Izhboldin modifies a conjecture of Lam and asks whether two quadratic forms, each of which isomorphic to the product of an Albert form and a kk-fold Pfister form, are similar provided they are equivalent modulo Ik+3I^{k+3}. We relate this conjecture to another conjecture on the dimensions of anisotropic forms in Ik+3I^{k+3}. As a consequence, we obtain that Izhboldin's conjecture is true for k1k\leq 1.

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Detlev W. Hoffmann, On a conjecture of Izhboldin on similarity of quadratic forms. Doc. Math. 4 (1999), pp. 61–64

DOI 10.4171/DM/53