Hoffmann, Detlev W.

On a conjecture of Izhboldin on similarity of quadratic forms

Doc. Math., J. DMV 4, 61-64 (1999)

Summary

Summary: 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 $k\leq 1$.

Mathematics Subject Classification

11E81, 11E04

Keywords/Phrases

quadratic form, Pfister form, Albert form, similarity of quadratic forms

Downloads