Detlev W. Hoffmann and Ahmed Laghribi: Isotropy of quadratic forms over the function field of a quadric in characteristic 2

detlev@math.univ-fcomte.fr laghribi@Mathematik.Uni-Bielefeld.DE

Submission: 2003, Dec 18

We extend to characteristic $2$ a theorem by the first author which states that if $\phi$ and $\psi$ are anisotropic quadratic forms over a field $F$ such that $\dim\phi\leq 2^n < \dim\psi$ for some nonnegative integer $n$, then $\phi$ stays anisotropic over the function field $F(\psi)$ of $\psi$. The case of singular forms is systematically included. We give applications to the characterization of quadratic forms with maximal splitting. We also prove a characteristic $2$ version of a theorem by Izhboldin on the isotropy of $\phi$ over $F(\psi)$ in the case $\dim\phi = 2^n+1 \leq\dim\psi$.

2000 Mathematics Subject Classification: Primary 11E04, Secondary 11E81

Keywords and Phrases: Quadratic forms, function field of a quadratic form, Pfister forms, Pfister neighbors, dominated quadratic forms, standard splitting of a quadratic form, maximal splitting.

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