On a Conjecture of Izhboldin on Similarity of Quadratic Forms

In his paper {\it Motivic 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 $k$-fold Pfister form, are similar provided they are equivalent modulo $I^{k+3}$. We relate this conjecture to another conjecture on the dimensions of anisotropic forms in $I^{k+3}$. As a consequence, we obtain that Izhboldin's conjecture is true for $k\leq 1$.

1991 Mathematics Subject Classification: Primary 11E81; Secondary 11E04.

Keywords and Phrases: Quadratic form, Pfister form, Albert form, similarity of quadratic forms.

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